Oscillator

ABSTRACT

An oscillator in which crosstalk can be reduced is provided. An oscillator includes a SQUID, a transmission line connected to the SQUID, a ground plane, and a first connection circuit disposed in a vicinity of a node of an electric field of a standing wave that is generated when the oscillator is oscillating, the first connection circuit connecting parts of the ground plane located on both sides of the transmission line to each other.

INCORPORATION BY REFERENCE

This application is a Continuation of U.S. Application No. 17/573,841,filed on Jan. 12, 2022, which is based upon and claims the benefit ofpriority from Japanese patent application No. 2021-12488, filed on Jan.28, 2021, the disclosure of which is incorporated herein in its entiretyby reference.

TECHNICAL FIELD

The present disclosure relates to an oscillator, and in particular to atechnique for reducing crosstalk in a superconducting quantum circuit.

BACKGROUND ART

How to reduce crosstalk in a chip of a quantum circuit where a pluralityof quantum bits are integrated is an important problem to be solved.Note that crosstalk means a phenomenon in which, for example, when acontrol signal is input to a given quantum bit, that control signalcouples with another quantum bit for some reason and hence the otherquantum bit is also unintentionally controlled. Specifically, forexample, it is a phenomenon in which the resonance frequency of theother quantum bit is changed. In experiments, crosstalk is also observedwhen a DC (Direct Current) control signal is input to a quantum bit aswell as when a control signal having a high frequency such as 20 GHz isinput to a quantum bit.

A chip of a superconducting quantum circuit is manufactured by using,for example, a coplanar waveguide structure. Published JapaneseTranslation of PCT International Publication for Patent Application, No.2018-524795 discloses a technique by which crosstalk in such a quantumcircuit chip can be reduced. In the configuration disclosed in thisdocument, GNDs (grounds) on both sides of a core line of a coplanarwaveguide are kept at potentials equal to each other by electricallyconnecting the GNDs on both sides of the core line by using an airbridge. In this way, a slot line mode is suppressed and, as a result,crosstalk can be reduced.

SUMMARY

However, research and development regarding superconducting quantumcircuits are still being conducted, so it has been required to providenew technologies for reducing crosstalk.

The present disclosure has been made to solve the above-describedproblem, and an example object thereof is to provide an oscillator inwhich crosstalk can be reduced.

In a first example aspect, an oscillator includes:

-   a SQUID (Superconducting QUantum Interference Device);-   a transmission line connected to the SQUID;-   a ground plane; and-   a first connection circuit disposed in a vicinity of a node of an    electric field of a standing wave that is generated when the    oscillator is oscillating, the first connection circuit connecting    parts of the ground plane located on both sides of the transmission    line to each other.

BRIEF DESCRIPTION OF DRAWINGS

The above and other aspects, features and advantages of the presentdisclosure will become more apparent from the following description ofcertain example embodiments when taken in conjunction with theaccompanying drawings, in which:

FIG. 1 shows a chip layout on a 2-bit distributed constant-typesuperconducting quantum circuit;

FIG. 2 shows an equivalent circuit of a 2-bit distributed constant-typesuperconducting quantum circuit;

FIG. 3A is an enlarged view of a part of the chip layout of the 2-bitdistributed constant-type superconducting quantum circuit in thevicinity of a SQUID thereof;

FIG. 3B is an enlarged view of a part of the chip layout of the 2-bitdistributed constant-type superconducting quantum circuit in thevicinity of the SQUID thereof;

FIG. 4 is a graph showing a result of a simulation in which a controlsignal having a frequency of 20 GHz is input to a first quantum bit froma control line of the first quantum bit;

FIG. 5 shows a chip layout in a case where air bridges are disposed overthe entire λ/4 line at intervals equal to or shorter than ⅒ of awavelength corresponding to 20 GHz;

FIG. 6 is a graph showing a result of a simulation in which air bridgesare disposed over the entire λ/4 line and a control signal having afrequency of 20 GHz is input to a first quantum bit from a control lineof the first quantum bit;

FIG. 7 shows a chip layout of a superconducting circuit according to afirst example embodiment;

FIG. 8 shows an equivalent circuit of a superconducting circuitaccording to the first example embodiment;

FIG. 9 is an enlarged view of a part of the chip layout of thesuperconducting circuit according to the first example embodiment in thevicinity of a first quantum bit thereof;

FIG. 10A is an enlarged view of a part of the chip layout of thesuperconducting quantum circuit according to the first exampleembodiment in the vicinity of a SQUID thereof;

FIG. 10B is an enlarged view of a part of the chip layout of thesuperconducting quantum circuit according to the first exampleembodiment in the vicinity of the SQUID thereof;

FIG. 11 is a graph showing a result of a simulation in which a controlsignal having a frequency of 20 GHz is input to a first quantum bit froma control line of the first quantum bit in the superconducting circuitaccording to the first example embodiment;

FIG. 12 shows a chip layout of a superconducting circuit according to asecond example embodiment;

FIG. 13 is an enlarged view of the chip layout of the superconductingcircuit according to the second example embodiment in the vicinity of afirst quantum bit thereof;

FIG. 14 is an enlarged view of the chip layout of the superconductingcircuit according to the second example embodiment in the vicinity of aSQUID of a second quantum bit thereof;

FIG. 15 is a graph showing a result of a simulation in which a controlsignal having a frequency of 20 GHz is input to a first quantum bit froma control line of the first quantum bit in a superconducting circuitaccording to the second example embodiment;

FIG. 16A shows a layout of a second quantum bit in the quantum circuitshown in FIG. 1 ;

FIG. 16B shows an equivalent circuit of the second quantum bit in thequantum circuit shown in FIG. 1 ;

FIG. 16C shows a layout of a second quantum bit in the second exampleembodiment;

FIG. 16D shows an equivalent circuit of the second quantum bit in thesecond example embodiment;

FIG. 17A is a diagram for explaining an operation for setting aresonance frequency of a second quantum bit for which no air bridge isprovided;

FIG. 17B is a diagram for explaining an operation of the second quantumbit for which no air bridge is provided when a DC current causingcrosstalk is flowing in a GND plane;

FIG. 18A is a diagram for explaining an operation of setting a resonancefrequency of a second quantum bit according to in the second exampleembodiment;

FIG. 18B is a diagram for explaining an operation of the second quantumbit according to the second example embodiment when a DC current causingcrosstalk is flowing in a GND plane;

FIG. 19 shows six types of examples of configurations for whichsimulations were performed;

FIG. 20 is a graph showing results of the simulations for the six typesof configurations;

FIG. 21 shows a chip layout of a superconducting circuit according to asecond modified example of the second example embodiment;

FIG. 22 shows an equivalent circuit of the superconducting circuitaccording to the second modified example of the second exampleembodiment;

FIG. 23 is an enlarged view of a chip layout of a superconductingcircuit according to a third example embodiment in the vicinity of aSQUID of a first quantum bit thereof;

FIG. 24 shows an equivalent circuit of the superconducting circuitaccording to the third example embodiment;

FIG. 25 is an enlarged view of a chip layout of a superconductingcircuit according to a fourth example embodiment in the vicinity of aSQUID of a first quantum bit thereof;

FIG. 26 shows an equivalent circuit of the superconducting circuitaccording to the fourth example embodiment;

FIG. 27 shows an equivalent circuit of a lumped constant-typesuperconducting quantum bit;

FIG. 28 shows a layout of a lumped constant-type superconducting quantumbit;

FIG. 29 shows a layout of a lumped constant-type superconducting quantumbit according to a fifth example embodiment;

FIG. 30 shows another layout of the lumped constant-type superconductingquantum bit according to the fifth example embodiment;

FIG. 31 shows a layout of a lumped constant-type superconducting quantumbit according to a modified example of the fifth example embodiment;

FIG. 32 shows a layout of a lumped constant-type superconducting quantumbit according to a sixth example embodiment;

FIG. 33 shows a layout of a lumped constant-type superconducting quantumbit according to a seventh example embodiment;

FIG. 34 shows an equivalent circuit of a lumped constant-typesuperconducting quantum bit according to a first modified example of thefifth example embodiment;

FIG. 35 shows a layout of the lumped constant-type superconductingquantum bit according to the first modified example of the fifth exampleembodiment;

FIG. 36 shows another layout of the lumped constant-type superconductingquantum bit according to the first modified example of the fifth exampleembodiment;

FIG. 37 shows an equivalent circuit of a lumped constant-typesuperconducting quantum bit according to a second modified example ofthe fifth example embodiment;

FIG. 38 shows a layout of the lumped constant-type superconductingquantum bit according to the second modified example of the fifthexample embodiment;

FIG. 39 shows another layout of the lumped constant-type superconductingquantum bit according to the second modified example of the fifthexample embodiment;

FIG. 40 shows a layout of a chip on which a part of a quantum bitaccording to an eighth example embodiment is formed;

FIG. 41 shows a layout of a substrate on which a part of a quantum bitaccording to the eighth example embodiment is formed;

FIG. 42 is a cross-sectional diagram of a structure in which a chip onwhich a part of a quantum bit according to the eighth example embodimentis formed and a substrate are flip-chip connected to each other;

FIG. 43 shows a layout of a chip on which GND planes on both sides of acontrol line are connected to each other;

FIG. 44 shows a layout of a substrate in which GND planes on both sidesof a control line are connected to each other;

FIG. 45 shows a layout of a chip on which a U-shaped control line isused;

FIG. 46 shows a layout of a substrate in which a U-shaped control lineis used;

FIG. 47 shows a layout of a chip on which a straight control line isused;

FIG. 48 shows a layout of a substrate in which a straight control lineis used;

FIG. 49 is a diagram that is obtained by adding a drawing forexplanation in the layout shown in FIG. 41 ;

FIG. 50 is a diagram for explaining a problem that occurs when a currentcausing crosstalk is flowing in the GND plane of the substrate shown inFIG. 49 ;

FIG. 51 shows a layout of a substrate according to a ninth exampleembodiment;

FIG. 52 is a diagram for explaining an effect of a current that flows tothe GND plane of the substrate shown in FIG. 51 ;

FIG. 53 shows a layout of a substrate according to a first modifiedexample of the ninth example embodiment;

FIG. 54 is a cross-sectional diagram of a structure in which a chip anda substrate are flip-chip connected to each other by using bumps;

FIG. 55 shows a layout of a substrate according to a second modifiedexample of the ninth example embodiment;

FIG. 56 shows a layout of a substrate according to a third modifiedexample of the ninth example embodiment;

FIG. 57 shows a layout of a substrate according to another modifiedexample of the ninth example embodiment; and

FIG. 58 shows a layout of a substrate according to another modifiedexample of the ninth example embodiment.

EXAMPLE EMBODIMENT

In the following description, the Josephson junction means an elementhaving a structure in which a thin insulating film is sandwiched betweena first superconductor and a second superconductor. Further, a SQUID(Superconducting QUantum Interference Device) is a component in whichtwo Josephson junctions are connected in a loop by superconductinglines. Further, some or all of the circuits described hereinafter are,for example, formed by using lines (wiring lines) made of asuperconductor, and are used in an environment having a temperature of,for example, 10 mK (milli-Kelvin) in order to obtain a superconductingstate.

Preliminary Study

Firstly, a problem of crosstalk in a chip of a superconducting quantumcircuit in which a plurality of quantum bit are integrated will bedescribed.

As an example of a chip of a quantum circuit in which a plurality ofquantum bits are integrated, FIG. 1 shows a chip layout of a 2-bitdistributed constant-type superconducting quantum circuit. FIG. 2 showsan equivalent circuit of the 2-bit distributed constant-typesuperconducting quantum circuit shown in FIG. 1 . This 2-bit distributedconstant-type superconducting quantum circuit has a configuration inwhich a first quantum bit 1001 and a second quantum bit 1002 are coupledwith each other through a capacitor 1303. The first and second quantumbits 1001 and 1002 have configurations similar to each other. The firstquantum bit 1001 has a configuration in which each of two distributedconstant lines is connected to a respective one of both ends of a SQUID1102. Each of these distributed constant lines has a lengthcorresponding to ¼ of a wavelength corresponding to the operatingfrequency of the first quantum bit 1001, so they are referred to as λ/4lines 1103 a and 1103 b, respectively, hereinafter. When the operatingfrequency of the first quantum bit 1001 is about 10 GHz, the length ofeach of the λ/4 lines 1103 a and 1103 b is about 2 to 3 mm. A controlline 1104 is magnetically coupled with the SQUID 1102. In other words,the control line 1104 and the SQUID 1102 are magnetically coupled witheach other by their mutual inductance in a noncontact manner. Theresonance frequency of the first quantum bit 1001 can be set byinputting a DC control signal thereto from the control line 1104. In astate in which a DC control signal for setting the resonance frequencyto a certain frequency is being input to the control line 1104, it ispossible to make the first quantum bit 1001 oscillate by furtherinputting a control signal having a frequency twice the set resonancefrequency to the control line 1104. The operating frequency (the setresonance frequency) of the first quantum bit 1001 is, for example,about 10 GHz. Therefore, when the first quantum bit 1001 is operated, asignal in which a DC control signal and a high-frequency control signalhaving a frequency of about 20 GHz are superimposed is input to thefirst quantum bit 1001 from the control line 1104. The configuration andhow to operate the second quantum bit 1002 are similar to those of thefirst quantum bit 1001, and therefore detailed descriptions thereof areomitted.

In the configuration shown in the drawing, the first and second quantumbits 1001 and 1002 are located on a chip 1004 which is electricallyconnected to wiring lines on a printed circuit board (PCB) 1005 by usingbonding wires 1006. The second quantum bit 1002 includes a SQUID 1202, aλ/4 line 1203 a, and a λ/4 line 1203 b. A control line 1204 ismagnetically coupled with the SQUID 1202. Note that one end of the λ/4line 1103 a of the first quantum bit 1001 is connected to the SQUID1102, and the other end of the λ/4 line 1103 a is connected to acapacitor 1301. Further, one end of the λ/4 line 1103 b of the firstquantum bit 1001 is connected to the SQUID 1102, and the other end ofthe λ/4 line 1103 b is connected to the capacitor 1303. Similarly, oneend of the λ/4 line 1203 a of the second quantum bit 1002 is connectedto the SQUID 1202, and the other end of the λ/4 line 1203 a is connectedto a capacitor 1302. Further, one end of the λ/4 line 1203 b of thesecond quantum bit 1002 is connected to the SQUID 1202, and the otherend of the λ/4 line 1203 b is connected to the capacitor 1303. As shownin FIG. 2 , the SQUID 1102 is a component in which a Josephson junction1105 a and a Josephson junction 1105 b are connected in a loop, and bothends of the SQUID 1102 are connected to the λ/4 lines 1103 a and 1103 b,respectively. Similarly, the SQUID 1202 is a component in which aJosephson junction 1205 a and a Josephson junction 1205 b are connectedin a loop, and both ends of the SQUID 1202 are connected to the λ/4lines 1203 a and 1203 b, respectively.

FIG. 3A shows an enlarged view of a part of the first quantum bit 1001shown in FIG. 1 in the vicinity of the SQUID 1102 thereof. Further, FIG.3B shows an enlarged view of a part of the second quantum bit 1002 shownin FIG. 1 in the vicinity of the SQUID 1202 thereof. Only the firstquantum bit 1001 shown in FIG. 3A is described hereinafter, and thedescription of the second quantum bit 1002, which can be described in asimilar manner, is omitted.

The tip of the control line 1104 separates into a first branch line11041 and a second branch line 11042, of which the first branch line11041 is laid out near the SQUID 1102 so that it magnetically coupleswith the SQUID 1102. Meanwhile, the second branch line 11042 is laid outaway from the SQUID 1102 so that it does not magnetically couple withthe SQUID 1102.

The control line 1104 and the λ/4 lines 1103 a and 1103 b are formed asa coplanar waveguide. The GND (ground) plane 1106 is located around thelines formed as the coplanar waveguide. The first and second branchlines 11041 and 11042 are both connected to this GND plane 1106. Notethat by the above-described branching, the imbalance between thecurrents that flow from the control line 1104 to the parts of the GNDplane 1106 located on both sides of the control line 1104 is suppressed.

Note that, in FIG. 3A, a symbol 11031 a represents a core line of theλ/4 line 1103 a, and a symbol 11031 b represents a core line of the λ/4line 1103 b. Similarly, in FIG. 3B, a symbol 12031 a represents a coreline of the λ/4 line 1203 a, and a symbol 12031 b represents a core lineof the λ/4 line 1203 b. Further, in FIG. 3 b , symbols 12041 and 12042represent the first and second branch lines, respectively, of thecontrol line 1204, and a symbol 1206 represents the GND plane.

Crosstalk means a phenomenon in which, for example, when a DC controlsignal or a high-frequency control signal is input to the first quantumbit 1001 from the control line 1104, that control signal couples withthe SQUID 1202 of the second quantum bit 1002 for some reason and hencethe second quantum bit 1002 is affected by the control signal.Specifically, it means a phenomenon in which, for example, the resonancefrequency of the second quantum bit 1002 is changed.

In order to understand the cause of this crosstalk, we have carried outsimulations using electromagnetic-field analysis software. Note that thesimulations were performed by using ANSYS HFSS manufactured by AnsysJapan, Inc. The results of the simulations showed that when a controlsignal having a frequency of 20 GHz was input to the first quantum bit1001 from the control line 1104 thereof, a large current flowed alongthe λ/4 lines 1103 a, 1103 b, 1203 b and 1203 a. Further, the followingresults were also obtained. FIG. 4 is a graph showing a current thatflows in the SQUID 1102 of the first quantum bit 1001 and a current thatflows in the SQUID 1202 of the second quantum bit 1002 when a controlsignal having a frequency of 20 GHz is input to the first quantum bit1001 from the control line 1104 thereof. Note that, in the graph shownin FIG. 4 , the horizontal axis indicates the phase of the controlsignal. The vertical axis indicates the amount of the current. As shownin FIG. 4 , a current that changes in a sine wave according to the phaseflows through the SQUID 1102 of the first quantum bit 1001. Note thatthe vertical axis in FIG. 4 has been normalized so that the maximumvalue becomes one. Since the SQUID 1102 of the first quantum bit 1001 isdesigned so as to magnetically couple with the control line 1104, theflow of the current through the SQUID 1102 of the first quantum bit 1001is the intended behavior. However, as shown in FIG. 4 , a current alsoflows through the SQUID 1202 of the second quantum bit 1002, whichshould not flow therethrough in the design. The maximum value of thecurrent flowing through the SQUID 1202 of the second quantum bit 1002 is0.32, which means that a current as large as 32 % of the current flowingthrough the SQUID 1102 of the first quantum bit 1001 flows through theSQUID 1202 of the second quantum bit 1002. That is, it can be understoodthat the SQUID 1202 of the second quantum bit 1002 is affected byhigh-frequency crosstalk.

The results shown in FIG. 4 indicate that when a high-frequency controlsignal having a frequency of 20 GHz is input from the control line 1104,a high-frequency electromagnetic field propagates along the λ/4 lines1103 a, 1103 b, 1203 b and 1203 a. It is considered that this phenomenonis caused by the occurrence of a potential difference between the GNDplanes 1106 and 1206 located on both sides of the core lines 11031 a,11031 b, 12031 b and 12031 a of the λ/4 lines 1103 a, 1103 b, 1203 b and1203 a, which should desirably be at potentials equal to each other.Therefore, in order to solve the above-described problem, the GND planes1106 and 1206 located on both sides of the core lines 11031 a, 11031 b,12031 b and 12031 a of the λ/4 lines 1103 a, 1103 b, 1203 b and 1203 ashould be short-circuited to each other. Specifically, as mentioned, forexample, in Published Japanese Translation of PCT InternationalPublication for Patent Application, No. 2018-524795, it is consideredthat this short-circuiting can be accomplished by providing air bridgesat places along the λ/4 lines 1103 a, 1103 b, 1203 b and 1203 a.Further, regarding the interval between the air bridges, for example,there is a method in which the interval is made sufficiently shorterthan the wavelength of an electromagnetic field that propagates throughthe quantum bit. Since the frequency of the control signal in theexample examined here is 20 GHz, the aforementioned wavelength on asilicon substrate is about 5.9 mm. A case where air bridges are providedat intervals sufficiently shorter than this wavelength, for example, atintervals of 600 µm (about ⅒ of the wavelength) or shorter will beexamined hereinafter. Note that the air bridge is a structure made of aconductive material such as a metal, and is a structure for electricallyconnecting GND planes located on both sides of a core line to eachother. The air bridge has such a structure that it is not in contactwith the core line, and intersects the core line in a three-dimensionalmanner (i.e., like an overpass). Therefore, the air bridge and the coreline are not electrically connected to each other. Typically, the spacebetween the air bridge and the core line is filled with air or is avacuum. In the case of a superconducting quantum circuit, the spacebetween the air bridge and the core line is a vacuum. However, since anair bridge is typically manufactured by using a semiconductor processtechnology, there is a possibility that some dielectric material such asa resist may remain near the air bridge during the manufacturing of theair bridge.

FIG. 5 shows a chip layout in which air bridges 1107 a to 1107 m and airbridges 1207 a to 1207 m are provided for λ/4 lines 1103 a, 1103 b, 1203b and 1203 a at intervals sufficiently shorter than the wavelengthcorresponding to the frequency of 20 GHz based on the above-describedconcept. Further, FIG. 6 also shows a result of a simulation in which acontrol signal having a frequency of 20 GHz is input to the firstquantum bit 1001 from the control line 1104 thereof in the configurationshown in FIG. 5 . By the provision of the air bridges 1107 a to 1107 mand 1207 a to 1207 m, the current flowing along the λ/4 lines 1103 a,1103 b, 1203 b and 1203 a was suppressed. As a result, as shown in FIG.6 , the current flowing through the SQUID 1202 of the second quantum bit1002 was reduced to about 1% of the current flowing through the SQUID1102 of the first quantum bit 1001. Therefore, it can be understood thatit is possible to significantly reduce the high-frequency crosstalk byproviding a plurality of air bridges 1107 a to 1107 m and 1207 a to 1207m over the entire λ/4 lines 1103 a, 1103 b, 1203 b and 1203 a atintervals sufficiently shorter than the wavelength of the controlsignal.

However, when air bridges are formed over the entire λ/4 lines 1103 a,1103 b, 1203 b and 1203 a, there is a possibility that the Q-value (theQuality factor) of the quantum bit could deteriorate. One possible causeof this deterioration is a dielectric loss caused by a dielectricmaterial such as a resist that remains when the air bridge ismanufactured. A standing wave occurs in a quantum bit during theoperation of the quantum bit. Since this standing wave is formed overthe entire quantum bit, an electric field is also generated on the λ/4lines during the operation of the quantum bit. Therefore, if air bridgesare formed over the entire λ/4 lines 1103 a, 1103 b, 1203 b and 1203 a,an electric field generated on the λ/4 lines spreads into the inside ofa dielectric material that remains near the air bridges, so that thedielectric loss in the dielectric material could cause a deteriorationof the Q-value. Therefore, an example embodiment in which crosstalk canbe reduced while preventing the Q-value of the quantum bit fromdeteriorating will be described.

First Example Embodiment

FIG. 7 shows a chip layout of a 2-bit distributed constant-typesuperconducting quantum circuit in which two superconducting circuits(oscillators) each of which is one according to a first exampleembodiment are integrated. Since the superconducting circuit describedhere oscillates, it is also referred to as an oscillator. FIG. 8 showsan equivalent circuit of the 2-bit distributed constant-typesuperconducting quantum circuit shown in FIG. 7 . The superconductingcircuit according to the first example embodiment is a superconductingquantum bit, and in particular, is a first quantum bit 1 or a secondquantum bit 2 in the equivalent circuit shown in FIG. 8 . The 2-bitdistributed constant-type superconducting quantum circuit shown in FIGS.7 and 8 has a configuration in which the first and second quantum bits 1and 2 are coupled through a capacitor 303. The first and second quantumbits 1 and 2 have configurations similar to each other.

The first quantum bit 1 has a configuration in which each of twodistributed constant lines (transmission lines) is connected to arespective one of both ends of a SQUID 102. Each of these distributedconstant lines has a length corresponding to ¼ of a wavelengthcorresponding to the operating frequency (the resonance frequency) ofthe first quantum bit 1, so they are referred to as λ/4 lines 103 a and103 b, respectively, hereinafter. When the operating frequency of thefirst quantum bit 1 is about 10 GHz, the length of each of the λ/4 lines103 a and 103 b is about 2 to 3 mm. A control line 104 is magneticallycoupled with the SQUID 102. In other words, the control line 104 and theSQUID 102 are magnetically coupled with each other by their mutualinductance in a noncontact manner. The resonance frequency of the firstquantum bit 1 can be set by inputting a DC control signal thereto fromthe control line 104. In a state in which a DC control signal forsetting the resonance frequency to a certain frequency is being input tothe control line 104, it is possible to make the first quantum bit 1oscillate by further inputting a control signal having a frequency twicethe set resonance frequency to the control line 104. The operatingfrequency (the set resonance frequency) of the first quantum bit 1 is,for example, about 10 GHz. Therefore, when the first quantum bit 1 isoperated, a signal in which a DC control signal and a high-frequencycontrol signal having a frequency of about 20 GHz are superimposed isinput to the first quantum bit 1 from the control line 104. Theconfiguration and how to operate the second quantum bit 2 are similar tothose of the first quantum bit 1, and therefore detailed descriptionsthereof are omitted.

In the configuration shown in FIG. 7 , the first and second quantum bits1 and 2 are located on a chip 4 that is electrically connected to wiringlines on a printed circuit board 5 by using bonding wires 6. The secondquantum bit 2 includes a SQUID 202, a λ/4 line 203 a, and a λ/4 line 203b. A control line 204 is magnetically coupled with the SQUID 202. Notethat one end of the λ/4 line 103 a of the first quantum bit 1 isconnected to one end of the SQUID 102, and the other end of the λ/4 line103 a is connected to a capacitor 301. Further, one end of the λ/4 line103 b of the first quantum bit 1 is connected to the other end of theSQUID 102, and the other end of the λ/4 line 103 b is connected to thecapacitor 303. Similarly, one end of the λ/4 line 203 a of the secondquantum bit 2 is connected to one end of the SQUID 202, and the otherend of the λ/4 line 203 a is connected to a capacitor 302. Further, oneend of the λ/4 line 203 b of the second quantum bit 2 is connected tothe other end of the SQUID 202, and the other end of the λ/4 line 203 bis connected to the capacitor 303.

As shown in FIG. 8 , the SQUID 102 is a component in which a Josephsonjunction 105 a and a Josephson junction 105 b are connected in a loop,and both ends of the SQUID 102 are connected to the λ/4 lines 103 a and103 b, respectively. Similarly, the SQUID 202 is a component in which aJosephson junction 205 a and a Josephson junction 205 b are connected ina loop, and both ends of the SQUID 202 are connected to the λ/4 lines203 a and 203 b, respectively. Further, as will be described later, inthis example embodiment, an air bridge 107 (see FIG. 7 ) is provided ata predetermined place for the first quantum bit 1, and an air bridge 207(see FIG. 7 ) is provided in a predetermined place for the secondquantum bit 2.

FIG. 9 shows an enlarged view of the vicinity of the first quantum bit 1in the chip layout shown in FIG. 7 . Further, FIG. 10A shows an enlargedview of the vicinity of the SQUID 102 of the first quantum bit 1 in thechip layout shown in FIG. 7 . Further, FIG. 10B shows an enlarged viewof the vicinity of the SQUID 202 of the second quantum bit 2 in the chiplayout shown in FIG. 7 .

Only the first quantum bit 1 is described hereinafter, and thedescription of the second quantum bit 2, which can be described in asimilar manner, is omitted. The tip of the control line 104 separates,at a branch point 108, into a first branch line 1041 and a second branchline 1042, of which the first branch line 1041 is laid out near theSQUID 102 so that it magnetically couples with the SQUID 102. Meanwhile,the second branch line 1042 is laid out away from SQUID 102 so that itdoes not magnetically couple with the SQUID 102. Specifically, in orderto make the first branch line 1041 magnetically couple with the SQUID102 while preventing the second branch line 1042 from magneticallycoupling with the SQUID 102, the first branch line 1041 is wired (e.g.,routed) along the SQUID 102, and the second branch line 1042 is wired inthe direction opposite to the direction in which the first branch line1041 is wired.

The control line 104 and the λ/4 lines 103 a and 103 b are formed as acoplanar waveguide. A GND plane 106 is located around the lines formedas the coplanar waveguide. The first and second branch lines 1041 and1042 are both connected to this GND plane 106.

Note that, in the drawings, a symbol 1031 a represents a core line ofthe λ/4 line 103 a, and a symbol 1031 b represents a core line of theλ/4 line 103 b. Further, a symbol 2031 a represents a core line of theλ/4 line 203 a, and a symbol 2031 b represents a core line of the λ/4line 203 b. Further, symbols 2041 and 2042 represent first and secondbranch lines, respectively, of the control line 204, and a symbol 208represents a branch point thereof. Further, a symbol 206 represents aGND plane.

The difference between the superconducting quantum bit according to thefirst example embodiment and the superconducting quantum bit describedabove with reference to FIGS. 3A and 3B lies in their layouts.Specifically, the arrangement of air bridges in the superconductingquantum bit according to the first example embodiment differs from thatin the superconducting quantum bit described above with reference toFIGS. 3A and 3B. As shown in FIGS. 9 and 10A, in the first quantum bit 1according to the first example embodiment, air bridges 107A and 107B areprovided, on the λ/4 lines 103A and 103B, only in the vicinity of a nodeof the electric field of a standing wave that is generated in thequantum bit during the operation of the quantum bit. That is, for theλ/4 lines 103 a and 103 b, the air bridges 107 a and 107 b are providedonly in the vicinity of the node of the electric field of the standingwave that is generated when the superconducting quantum bit (theoscillator) is oscillating. In other words, on the λ/4 lines 103 a and103 b, the air bridges 107 a and 107 b are provided only in the vicinityof the parts of the λ/4 lines 103 a and 103 b at which they areconnected to the SQUID 102 (hereinafter also referred to as connectionparts with the SQUID 102). In yet other words, on the λ/4 lines 103 aand 103 b, the air bridges 107 a and 107 b are provided only in thevicinity of the parts of the λ/4 lines 103 a and 103 b that are furthestfrom the parts thereof at which they are connected to the capacitors 301and 303 (hereinafter also referred to as connection parts with thecapacitors 301 and 303). Specifically, on the λ/4 lines 103 a and 103 b,the air bridges 107 a and 107 b are preferably provided only at placesthat are as close as possible to the connection parts with the SQUID102. For example, on the λ/4 lines 103 a and 103 b, the air bridges 107a and 107 b are preferably provided only at places 1/20 or less of thelength of the λ/4 line 103 a or 103 b from the connection parts with theSQUID 102. More preferably, on the λ/4 lines 103 a and 103 b, the airbridges 107 a and 107 b are provided only at places 1/30 or less of thelength of the λ/4 line 103 a or 103 b from the connection parts with theSQUID 102. In the example shown in FIGS. 9 and 10A, on the λ/4 lines 103a and 103 b, the air bridges 107 a and 107 b are provided only at placesabout 60 µm from the connection parts with the SQUID 102 (i.e., only atplaces on the λ/4 lines 103 a and 103 b that are at a distance of about1/30 of the length of the λ/4 line 103 a or 103 b from the connectionparts with the SQUID 102).

In this example embodiment, the length of the air bridge, i.e., thelength from the part where one end of the air bridge is connected to theGND plane to the part where the other end of the air bridge is connectedto the GND plane, is preferably as short as possible. Specifically, thelength of the air bridge is preferably equal to or shorter than ⅒ of thewavelength of a high-frequency control signal input from the controlline on the chip, more preferably equal to or shorter than 1/30 thereof,and even more preferably equal to or shorter than 1/50 thereof. Forexample, when the frequency of the control signal is 20 GHz, thewavelength of the control signal on the chip is about 5.9 mm. Therefore,in this case, the length of the air bridge is preferably equal to orshorter than 590 µm, more preferably equal to or shorter than 196 µm,and even more preferably equal to or shorter than 118 µm.

Note that the above-described preferred lengths of the air bridge alsoapply to all the example embodiments described in this specificationother than the first example embodiment, and to all the modifiedexamples thereof described in this specification. Note that, in thisexample embodiment, the length of the air bridge was set to 62 µm. Thislength is about 1/95 of the wavelength of the control signal having afrequency of 20 GHz on the chip. The length of the air bridge was alsoset to 62 µm in all the example embodiments described in thisspecification other than the first example embodiment and all themodified examples thereof.

The standing wave generated in the first quantum bit 1 during theoperation of the first quantum bit 1 forms antinodes of the electricfield, on the λ/4 lines 103 a and 103 b, near the connection parts withthe capacitors 301 and 303, and forms a node of the electric field, onthe λ/4 lines 103 a and 103 b, near the connection parts with the SQUID102. In other words, on the λ/4 lines 103 a and 103 b, the amplitude ofthe electric field is the largest near the connection parts with thecapacitors 301 and 303, and the amplitude of the electric fielddecreases as the distance from the capacitors 301 and 303 increases.Further, the amplitude of the electric field is the smallest near theconnection parts with the SQUID 102. In the first example embodiment,the air bridges 107 a and 107 b are provided, on the λ/4 lines, only inthe vicinity of the node of the electric field of the standing wave,i.e., in the vicinity of the place where the electric field is theweakest. In this way, most of the components of the electric field ofthe standing wave that is generated in the first quantum bit 1 duringthe operation of the first quantum bit 1 are far from the air bridges107 a and 107 b. Therefore, even in the case where a dielectric materialsuch as a resist remains in the air bridges 107 a and 107 b, it ispossible to reduce the electric field that spreads into the residue asmuch as possible. Therefore, it is possible to reduce the dielectricloss, and as a result, to prevent the Q-value of the first quantum bit 1from deteriorating. Note that although it is not described, air bridges207 a and 207 b are arranged in the second quantum bit 2 in a mannersimilar to that of the first quantum bit 1.

As shown in FIG. 9 , in the superconducting circuit according to thefirst example embodiment, in addition to the air bridges 107 a and 107 bprovided on the λ/4 lines, air bridges 107 c to 107 h are also providedat arbitrary places on the control line 104. Since the control line 104,which extends in a direction different from the direction of the λ/4lines 103 a and 103 b, is far from the λ/4 lines 103 a and 103 b, theprovision of the air bridges 107 c to 107 h on the control line 104 doesnot directly affect the Q-value of the first quantum bit 1. In otherwords, the disposition of the air bridges 107 c to 107 h on the controlline 104 does not cause a deterioration of the Q-value of the firstquantum bit 1. Note that, more specifically, the air bridges 107 c to107 h are provided in the non-branched part of the control line 104other than the first and second branch lines 1041 and 1042 thereof. Inthis example embodiment, an air bridge 207 c and the like are providedon the control line 204 of the second quantum bit 2 in a similar manner.

As described above, in this example embodiment, the air bridges 107 a,107 b, 207 a and 207 b are provided only in the vicinity of the node ofthe electric field on the λ/4 lines 103 a, 103 b, 203 a and 203 b. Inthis way, it is possible to reduce high-frequency crosstalk whilepreventing the Q-values of the first and second quantum bits 1 and 2from deteriorating. Results of simulations will be describedhereinafter. FIG. 11 shows a result of a simulation in which a controlsignal having a frequency of 20 GHz is input to the first quantum bit 1from the control line 104 thereof in the configuration according to thefirst example embodiment. As shown in FIG. 11 , the current flowingthrough the SQUID 202 of the second quantum bit 2 was equal to orsmaller than 1% of the current flowing through the SQUID 102 of thefirst quantum bit 1. This means that the use of the superconductingcircuit according to the first example embodiment provides anadvantageous effect that the high-frequency crosstalk can be reducedwhile preventing the Q-value of the quantum bit from deteriorating.

Note that the above-described superconducting circuit, i.e., theoscillator, can also be expressed as follows. The oscillator includes aSQUID, transmission lines (distributed constant lines) connected to theSQUID, a GND plane, and a connection circuit. Note that the connectioncircuit is a circuit that connects parts of the GND plane located onboth sides of the transmission line to each other, and theabove-described air bridge that connects parts of the GND plane acrossthe transmission line correspond to this connection circuit. Further,this connection circuit is disposed in a place corresponding to thevicinity of the node of the electric field of a standing wave that isgenerated when the oscillator is oscillating. According to theabove-described configuration, it is possible to reduce the crosstalkwhile preventing the Q-value of the quantum bit from deteriorating. Notethat a connection circuit (an air bridge) may also be provided for thecontrol line, which magnetically couples with the SQUID and to which acontrol signal is input, in order to reduce the crosstalk. That is, theoscillator may further include a connection circuit that connects partsof the GND plane located on both sides of the control line to each other(a circuit that connects parts of the GND plane across the control line,such as the air bridge 107 c).

Second Example Embodiment

Next, a second example embodiment will be described. Note thatdescriptions of the components similar to those in the first exampleembodiment are omitted as appropriate. FIG. 12 shows a chip layout of a2-bit distributed constant-type superconducting quantum circuit, inwhich two superconducting circuits (oscillators) each of which is oneaccording to a second example embodiment are integrated. Theconfiguration in the vicinity of the SQUIDs 102 and 202 in the chiplayout shown in FIG. 12 differs from that in the first exampleembodiment. This difference will be described later by using an enlargedview. The superconducting circuit according to the second exampleembodiment is a superconducting quantum bit, and its equivalent circuitis similar to that shown in FIG. 8 , so the description of theequivalent circuit is omitted here. The chip layout shown in FIG. 12 isone that is obtained by laying out, on a chip, a 2-bit distributedconstant-type superconducting quantum circuit formed by coupling twoquantum bits according to the second example embodiment with each otherthrough a capacitor 303.

The difference between the superconducting quantum bit according to thesecond example embodiment and that according to the first exampleembodiment lies in the arrangement of air bridges. FIG. 13 shows anenlarged view of the vicinity of the first quantum bit 1 in the chiplayout shown in FIG. 12 . As shown in FIG. 13 , similarly to the firstexample embodiment, in the superconducting circuit according to thesecond example embodiment, air bridges 107 a and 107 b are provided, onthe λ/4 lines 103 a and 103 b, only at places that are as close aspossible to the connection parts with the SQUID 102, and air bridges 107c to 107 h are also provided for the control line 104. However, thesecond example embodiment differs from the first example embodimentbecause a certain restriction is imposed on the positions of the airbridges 107 a and 107 b provided on the λ/4 lines 103 a and 103 b. Thisrestriction will be described hereinafter. FIG. 14 shows an enlargedview of the vicinity of the SQUID 202 of the second quantum bit 2 in thechip layout shown in FIG. 12 . Note that the positions of the airbridges 107 a and 107 b for the first quantum bit 1 are similar to thoseof the air bridges 207 a and 207 b for the second quantum bit 2.

Although the air bridges 207 a and 207 b provided in the first exampleembodiment do not have to be disposed at equal distances from the branchpoint 208 of the control line 204 as shown in FIG. 10B. In contrast, inthe second example embodiment, as shown in FIG. 14 , the air bridges 207a and 207 b are provided at equal distances from the branch point 208 ofthe control line 204. In other words, the air bridges 207 a and 207 bare provided at the ends of the first and second branch lines 2041 and2042, respectively, which have lengths equal to each other, i.e., atplaces on the first and second branch lines 2041 and 2042, respectively,at which they are connected to the ground, i.e., to the GND plane 206.Specifically, as shown in FIG. 14 , in the second example embodiment,the air bridges 207 a and 207 b are provided, on the λ/4 lines 203 a and203 b, at two places that are at equal distances from the branch point208 of the control line 204. Note that they are at equal distances onlyin ideal cases, and in practice, the term “equal distances” includesmanufacturing errors equal to or smaller than ±10%. That is, thedifference between their distances may be equal to or smaller than 10%of the length of either one of them. As described above, in this exampleembodiment, it is sufficient if the air bridges 207 a and 207 b areprovided at roughly equal distances from the branch point 208. In thefirst example embodiment, it is specified only that the air bridges 207a and 207 b, which are provided in the vicinity of the connection partswith the SQUID 202 on the λ/4 lines 203 a and 203 b, should be providedas close as possible to the SQUID 202. Therefore, as shown in FIG. 10B,the positions of the two air bridges 207 a and 207 b in the vicinity ofthe connection parts with the SQUID 202 on the λ/4 lines 203 a and 203 bdo not necessarily have to be at equal distances from the branch point208 of the control line 204. The above-described point is the differencebetween the first and second example embodiments.

Note that the first and second branch lines 2041 and 2042 are arrangedso that the amounts of the currents flowing through the first and secondbranch lines 2041 and 2042 are equal to each other and these currentsflow in directions opposite to each other. Specifically, as shown in thedrawing, the first and second branch lines 2041 and 2042 haveconfigurations symmetrical to each other in the left/right direction.The first branch line 2041 is wired (i.e., routed) along the SQUID 202,and the second branch line 2042 is wired in the direction opposite tothat of the first branch line 2041. Therefore, they are configured sothat the first branch line 2041 magnetically couples with the SQUID 202while the second branch line 2042 does not magnetically couple with theSQUID 202. More specifically, for example, as shown in FIG. 14 , thecontrol line 204 is a T-shaped line, and the first and second branchlines 2041 and 2042, which separate at the branch point 208, arearranged in a straight line (i.e., aligned with each other). That is,the angle between the first branch line 2041 and the non-branched partof the control line 204 is 90 degrees, and the angle between the secondbranch line 2042 and the non-branched part of the control line 204 is 90degrees. Further the angle between the first and second branch lines2041 and 2042 is 180 degrees. These angles are values in ideal cases,and in practice, they include manufacturing errors equal to or smallerthan ±10% of these ideal angles.

Note that the positional relationship among the SQUID 202, the λ/4 lines203 a and 203 b, and the control line 204 is, for example, as shown inFIG. 14 and will be described hereinafter. The λ/4 lines 203 a and 203 band the SQUID 202 are arranged in a first direction (the up/downdirection in the drawing) in the vicinity of the SQUID 202. Further, thefirst and second branch lines 2041 and 2042 are also wired in this firstdirection (the up/down direction in the drawing). Note that thenon-branched part of the control line 204 extends in a second direction(the left/right direction in the drawing) in the vicinity of the SQUID202, and extends from the branch point 208 so as to recede from theSQUID 202. That is, the non-branched part of the control line 204 iswired on the side of the branch point 208 opposite to the side thereofon which the SQUID 202 is located. The first branch line 2041 is locatedso as to be opposed to the SQUID 202, while the second branch line 2042is located so as to be not opposed to the SQUID 202.

The aim of the above-described configuration in the second exampleembodiment will be described later. Firstly, FIG. 15 shows a result of asimulation in which a control signal having a frequency of 20 GHz isinput to the first quantum bit 1 from the control line 104 thereof inthe second example embodiment. As shown in FIG. 15 , when ahigh-frequency control signal having a frequency of 20 GHz is input fromthe control line 104 of the first quantum bit 1, the current flowingthrough the SQUID 202 of the second quantum bit 2 is equal to or smallerthan 1% of the current flowing through the SQUID 102 of the firstquantum bit 1. That is, it can be understood that high-frequencycrosstalk can also be significantly reduced in the second exampleembodiment as in the case of the first example embodiment. This meansthat, similarly to the first example embodiment, the second exampleembodiment provides an advantageous effect that the high-frequencycrosstalk can be reduced while preventing the Q-value of the quantum bitfrom deteriorating.

Regarding Additional Advantage Effect of Second Example Embodiment

Next, the aim of the second example embodiment will be described. Themeans for reducing crosstalk when a high-frequency control signal suchas a control signal having a frequency of 20 GHz is input from thecontrol line has been described so far. However, in experiments,crosstalk is also observed when a DC control signal is input from thecontrol line. It is considered that this phenomenon is caused because,for example, the SQUID 202 of the second quantum bit 2 senses (i.e., isaffected by) a magnetic field that is generated when the DC controlsignal flows through the GND plane after flowing through the controlline 104 of the first quantum bit 1. That is, it is considered that themechanism due to which crosstalk is caused (in other words, the path andthe way of the propagation of the current that causes crosstalk) differsfrom the mechanism due to which the high-frequency crosstalk propagatingalong the λ/4 line is caused described above. The second exampleembodiment is an example embodiment for reducing not only thehigh-frequency crosstalk described above, but also DC crosstalk (moreprecisely, crosstalk that is caused as a current flows through the GNDplane). This example embodiment will be described hereinafter in detail.

FIG. 16A shows a layout of the second quantum bit 1002 in the quantumcircuit shown in FIG. 1 , i.e., the second quantum bit 1002 in which noair bridge is provided, and FIG. 16B shows its equivalent circuit.Further, FIG. 16C shows a layout of a second quantum bit 2 according tothe second example embodiment, and FIG. 16D shows its equivalentcircuit. As shown in FIGS. 16C and 16D, in the second exampleembodiment, air bridges 207 a and 207 b are disposed in the vicinity ofthe connection parts with the SQUID 202 on the λ/4 lines 203 a and 203 bso that they are equal distances from the branch point 208 of thecontrol line 204. In this way, a superconducting loop 209 (a loopcircuit indicated by dotted lines in FIGS. 16C and 16D) expressed as “aGND plane 206 - an air bridge 207 a -the GND plane 206 - a second branchline 2042 - a first branch line 2041 - the GND plane 206 - an air bridge207 b - the GND plane 206” is formed so as to surround the outside ofthe SQUID 202. That is, the superconducting loop 209 is a circuit madeof a superconductor using the GND plane 206, the air bridges 207 a and207 b, and the first and second branch lines 2041 and 2042. Note thatthe superconducting loop is also referred to as a superconducting loopcircuit. As described above, the first and second branch lines 2041 and2042 of the control line 204 are disposed on the superconducting loop209. One of the properties unique to superconductivity is that amagnetic flux that passes through the inside of a superconducting loopmust be conserved. The second example embodiment uses this propertyunique to superconductivity. Note that although it is not specificallyrestricted in the first example embodiment, the air bridges 207 a and207 b, the GND plane 206, and the control line 204 for the secondquantum bit 2 are made of a superconductor in this example embodiment asdescribed above. This restriction also applies to the first quantum bit1.

FIGS. 17A and 17B are diagrams for explaining operations (i.e.,behaviors) performed by the second quantum bit 1002 in which no airbridge is provided. FIG. 17A is a diagram for explaining an operation ofthe second quantum bit 1002 when the resonance frequency thereof is set,and FIG. 17B is a diagram for explaining an operation of the secondquantum bit 1002 when a DC current, which causes crosstalk, is flowingthrough the GND plane 1206.

Firstly, referring to FIG. 17A, in the case of the quantum bit 1002 inwhich no air bridge is provided, the control of the resonance frequencyof the quantum bit 1002 is performed as follows. That is, when a DCcontrol current (a control signal) I0 is input from the control line1204, the current I0 is divided into currents I1 and I2 that flow thefirst and second branch lines 12041 and 12042, respectively. As aresult, a part of a magnetic flux G1 generated by the current I1 passesthrough the loop of the SQUID 1202. One of the properties unique to aSQUID is that a magnetic flux that passes through the loop of the SQUIDmust be an integral multiple of the flux quantum. Therefore, when thepart of the magnetic flux G1 generated by the current I1 that passesthrough the loop of the SQUID 1202 is not exactly an integral multipleof the flux quantum, a circulating current flows through the SQUID 1202so that the total magnetic flux that passes through the loop of theSQUID 1202 becomes an integral multiple of the flux quantum. Themagnetic flux generated by this circulating current is indicated by asymbol G3 in the drawing. Note that the symbol G2 represents a magneticflux generated by the current I2. On the other hand, when the part ofthe magnetic flux G1 generated by the current I1 that passes through theloop of the SQUID 1202 is exactly an integral multiple of the fluxquantum, no circulating current flows through the SQUID 1202. As theamount and the direction of the control current I0 are changed, theamount and the direction of the current I1 are also changed, so that itis possible to change the magnitude and the direction of the part of themagnetic flux G1 generated by the current I1 that passes through theloop of the SQUID 1202, and thereby to change the amount and thedirection of the circulating current flowing through the SQUID 1202. Inthis way, it is possible to control the amount and the direction of thecirculating current flowing through the SQUID 1202, i.e., the currentflowing through the Josephson junctions 1205 a and 1205 b, bycontrolling the amount and the direction of the control current I0. Theequivalent inductance of a Josephson junction can be controlled by theamount of the current flowing through the Josephson junction. Therefore,it is possible to control the equivalent inductances of the Josephsonjunctions 1205 a and 1205 b by changing the amount and the direction ofthe control current I0. Therefore, it is possible to control theeffective inductance of the SQUID 1202, and thereby to control theresonance frequency of the second quantum bit 1002. That is, the totalinductance of the second quantum bit 1002, which is composed of theSQUID 1202 and the λ/4 lines 1203 a and 1203 b, can be changed bychanging the effective inductance of the SQUID 1202. Therefore, it ispossible to change the resonance frequency of the second quantum bit1002. Meanwhile, since the current I2 and the SQUID 1202 are far fromeach other, the magnetic flux G2 generated by the current I2 hardlypasses through the loop of the SQUID 1202. Note that since asuperconductor has a property called perfect diamagnetism, no magneticfield can pass through the superconductor. Therefore, a magnetic fieldcan pass through only places where no superconductor is present.Therefore, the magnetic flux G2 generated by the current I2 mainlypasses through the gap between the core lines 12031 a and 12031 b of theλ/4 lines 1203 a and 1203 b and the GND plane 1206, so that the magneticflux G2 generated by the current I2 does not affect the SQUID 1202 atall. The operations (i.e., behaviors) described so far are exactly theintended operations (i.e., behaviors).

Further, referring to FIG. 17B, a case where a DC current, which causescrosstalk, is flowing through the GND plane 1206 in the second quantumbit 1002 in which no air bridge provided will be examined. For thisexamination, for example, it is assumed that, in the 2-bit distributedconstant-type quantum circuit shown in FIG. 1 , the DC control currentinput to the first quantum bit 1001 flows from the control line 1104 tothe GND plane 1106 and then to the GND plane 1206. When a DC currentIR1, which causes crosstalk, is flowing in the GND plane 1206 as shownin FIG. 17B, a part of a magnetic flux G4 generated by the current IR1passes through the loop of the SQUID 1202. Since a circulating currentflows through the SQUID 1202 according to the magnitude and thedirection of the magnetic flux that passes through the loop of the SQUID1202 as described above, a current flows through Josephson junctions1205 a and 1205 b. As a result, the effective inductance of the SQUID1202 is changed due to the current IR1, and because of this change, theresonance frequency of the second quantum bit 1002 is changed. Theabove-described phenomenon is the mechanism due to which the DCcrosstalk is caused. Such DC crosstalk can be observed in the secondquantum bit 1002 when a DC control current is input to the first quantumbit 1001, and are also observed in experiments. Note that, in FIG. 17B,the magnetic flux generated by the circulating current is indicated by asymbol G5.

As a comparison to this, the operation (i.e., the behavior) of thesecond quantum bit 2 according to the second example embodiment will bedescribed. FIGS. 18 a and 18B are diagram for explaining operations (orbehaviors) performed by the second quantum bit 2 according to the secondexample embodiment. FIG. 18A is a diagram for explaining an operation ofthe second quantum bit 2 when the resonance frequency thereof is set,and FIG. 18B is a diagram for explaining an operation of the secondquantum bit 2 when a DC current, which causes crosstalk, is flowingthrough the GND plane 206.

Firstly, referring to FIG. 18A, the control of the resonance frequencyof the second quantum bit 2 according to the second example embodimentis performed as follows. That is, when a DC control current I0 issupplied from the control line 204, the current I0 is divided intocurrents I1 and I2 that flow the first and second branch lines 2041 and2042, respectively. As a result, a part of a magnetic flux G1 generatedby the current I1 passes through the loop of the SQUID 202. Since acirculating current flows through the SQUID 202 according to themagnitude and the direction of this magnetic flux which passes throughthe loop of the SQUID 202 as described above, a current flows throughJosephson junctions 205 a and 205 b. Therefore, the effective inductanceof the SQUID 202 can be controlled by changing the amount and thedirection of the control current I0. Therefore, it is possible tocontrol the resonance frequency of the second quantum bit 2. A magneticflux generated by this circulating current is indicated by a symbol G3in the drawing. Meanwhile, since the current I2 and the SQUID 202 arefar from each other, the magnetic flux G2 generated by the current I2hardly passes through the loop of the SQUID 202. The magnetic flux G2generated by the current I2 mainly passes through the gap between thecore lines 2031 a and 2031 b of the λ/4 lines 203 a and 203 b and theGND plane 206, so that the magnetic flux G2 generated by the current I2does not affect the SQUID 202 at all. Note that, in the second exampleembodiment, the air bridges 207 a and 207 b provided in the vicinity ofthe connection parts with the SQUID 202 on the λ/4 lines 203 a and 203 bare disposed so that they are at equal distances from the branch point208 of the control line 204. Therefore, the first and second branchlines 2041 and 2042 have shapes identical to each other, and haveinductances equal to each other. As mentioned above, there is a propertyunique to superconductivity, i.e., a property that a magnetic flux thatpasses through the inside of the superconducting loop 209 must beconserved. However, the amounts of the currents I1 and I2 are equal toeach other and their directions are opposite to each other. Therefore,the magnitudes of the magnetic flux G1 (Magnetic Flux = Current ×Inductance) generated by the current I1 and the magnetic flux G2generated by the current I2 in the area inside the superconducting loop209 are equal to each other, and their directions are opposite to eachother, so that they cancel each other. Therefore, the magnetic flux inthe area inside the superconducting loop 209 is conserved at zero (i.e.,remains at zero). Therefore, no shielding current is generated in thesuperconducting loop 209 even when the control current is input.Accordingly, the resonance frequency is not set (i.e., is not changed)to an unintended frequency.

Further, referring to FIG. 18B, a case where a DC current, which causescrosstalk, is flowing through the GND plane 206 in the second quantumbit 2 according to the second example embodiment will be examined. Whena DC current IR1, which causes crosstalk, is flowing in the GND plane206 as shown in FIG. 18B, a part of a magnetic flux G4 generated by thecurrent IR1 passes through the loop of the SQUID 202. However, asdescribed above, because of the property unique to superconductivity,i.e., the property that the magnetic flux inside the superconductingloop 209 must be conserved, a shielding current IS1 flows as shown inFIG. 18B. That is, the shielding current IS1 flows through the pathcomposed of the GND plane 206, the air bridge 207 b, the GND plane 206,the first branch line 2041, the second branch line 2042, the GND plane206, the air bridge 207 a, and the GND plane 206. A magnetic flux G6generated inside the superconducting loop 209 by the shielding currentIS1 is completely canceled by the magnetic flux generated inside thesuperconducting loop 209 by the current IR1. This is because of theproperty unique to superconductivity, i.e., the property that themagnetic flux in the superconducting loop must be conserved as describedabove. A part of the magnetic flux G6 generated by the shielding currentIS1 passes through the loop of the SQUID 202. The direction of themagnetic flux G4 generated in the loop of the SQUID 202 by the currentIR1, which causes crosstalk, and that of the magnetic flux G6 generatedin the loop of the SQUID 202 by the shielding current IS1 are oppositeto each other. Therefore, since the magnetic flux G4 generated by thecurrent IR1, which causes crosstalk, and the magnetic flux G6 generatedby the shielding current IS1 cancel each other inside the loop of theSQUID 202, the magnetic flux that passes through the loop of the SQUID202 becomes zero or very small. At least by the effect of the shieldingcurrent IS1, the magnetic flux that passes through the loop of the SQUID202 becomes smaller than the part of the magnetic flux generated by thecurrent IR1, which causes crosstalk, that passes through the loop of theSQUID 202. As a result, it is possible to reduce the changes in theeffective inductance of the SQUID 202 caused by current IR1, whichcauses crosstalk, i.e., the changes in the resonance frequency of thesecond quantum bit 2, by the effect of the shielding current IS1. Thatis, the DC crosstalk can be reduced.

As described above, in the second example embodiment, it is possible, inaddition to reducing the high-frequency crosstalk propagating along theλ/4 line while preventing the Q-value of the quantum bit fromdeteriorating, to reduce the DC crosstalk which is caused as the DCcurrent propagates through the GND plane.

Note that the control line 204 is preferably disposed so that noshielding current flows in the superconducting loop 209 due to thecontrol current (the control signal) of the control line. That is, asshown in this example embodiment, the control line 204 is preferablydisposed so that two types of magnetic fluxes of which the magnitudesare equal to each other and the directions are opposite to each otherpass through the superconducting loop 209 by the control current (thecontrol signal) flowing through the control line 204. Note that themagnitudes of these two types of magnetic fluxes do not have to beexactly equal to each other, and may include some errors. That is, thesetwo types of magnetic fluxes may be those having magnitudes roughlyequal to each other. For example, the difference between them may beequal to or smaller than 10% of the magnitude of either one of them.However, the configuration in which two types of magnetic fluxes ofwhich the magnitudes are roughly equal to each other and the directionsopposite to each other pass through the superconducting loop 209 is notindispensable, though it is preferred as a configuration for reducingthe effect of the current IR1, which causes crosstalk. Therefore, asuperconducting circuit, i.e., an oscillator, which can provide theabove-described advantageous effects can also be expressed as follows.The oscillator includes a SQUID, transmission lines (distributedconstant lines) connected to the SQUID, a GND plane, and a connectioncircuit. Note that two transmission lines are connected to the SQUID.Further, one of the transmission lines is connected to one end of theSQUID, and the other transmission line is connected to the other end ofthe SQUID. Further, the connection circuit is a circuit that connectsparts of the GND plane located on both sides of the transmission line toeach other. Further, the connection circuit is provided for each of thetwo transmission lines. This connection circuit is provided in thevicinity of a node of the electric field of a standing wave that isgenerated when the oscillator is oscillating. Further, a superconductingloop circuit using the GND plane and the connection circuit is providedin the oscillator so as to surround the SQUID thereof. According to theabove-described configuration, it is possible to reduce thehigh-frequency crosstalk propagating along the λ/4 line while preventingthe Q-value of the quantum bit from deteriorating, and to reduce the DCcrosstalk which is caused as the DC current propagates through the GNDplane.

It should be noted that, in this example embodiment, the inventorscarried out simulations for the position of an air bridge provided forthe control line 104. The results of the simulations for the position ofthe air bridge provided for the control line 104 will be describedhereinafter. The simulations were performed for a case where only oneair bridge is provided on the control line in the second exampleembodiment. In particular, how the crosstalk reduction effect changes asthe position of the air bridge provided on the control line is changedwas examined by the simulations. Note that, in the followingdescription, simulations for the first quantum bit will be described,and the description of simulations for the second quantum bit, fromwhich similar results can be obtained, will be omitted.

FIG. 19 shows six types of configurations for which simulations wereperformed. FIG. 19 shows six types of examples of configurations asexamples of configurations in the case where only one air bridge isprovided on the control line in the second example embodiment. In thesesix configuration examples, the distance from the branch point 108 ofthe control line 104 to the air bridge 107 c on the control line 104 ischanged from one configuration example to another. Specifically,simulations were performed for six types of cases in which the distancefrom the branch point 108 to the air bridge 107 c on the control line104 is about λ/4 (Case 1), about λ/6 (Case 2), about λ/10 (Case 3),about λ/20 (Case 4), about λ/50 (Case 5), and about λ/100 (Case 6). Notethat λ is the wavelength of a signal having a frequency of 20 GHz inputfrom the control line 104 on the chip, and is about 5.9 mm in thisexample embodiment. In each of the simulations, the percentage (%) ofthe current flowing through the SQUID 202 of the second quantum bit 2 tothe current flowing through the SQUID 102 of the first quantum bit 1when a control signal having a frequency of 20 GHz was input to thecontrol line 104 of the first quantum bit 1 was examined. The value ofthis percentage indicates as follows: the larger this percentage is, thelarger the effect of crosstalk is; and conversely, the smaller thispercentage is, the smaller the effect of crosstalk is (i.e., the largerthe crosstalk reduction effect is).

FIG. 20 shows the results of the simulations. FIG. 20 is a graph showingthe results of the simulations for the above-described six types ofcases. In the graph shown in FIG. 20 , the horizontal axis indicates thevalue that is obtained by dividing the distance (mm) from the branchpoint 108 of the control line 104 to the air bridge 107 c provided onthe control line 104 by the wavelength of a signal having a frequency of20 GHz on the chip (i.e., by 5.9 mm). Further, in FIG. 20 , the verticalaxis indicates the ratio, expressed as a percentage, of the currentflowing through the SQUID 202 of the second quantum bit 2 to the currentflowing through the SQUID 102 of the first quantum bit 1. Points plottedin FIG. 20 correspond to, from the right side to the left side, theaforementioned Case 1, Case 2, Case 3, Case 4, Case 5, and Case 6,respectively.

As can be understood from the results shown in FIG. 20 , when only oneair bridge is provided on the control line in the second exampleembodiment, the crosstalk reduction effect increases when the air bridgeprovided on the control line is located far from the branch point ascompared to when the air bridge is located close to the branch point ofthe control line. Note that it can be understood from FIG. 20 that inorder to make the crosstalk smaller than 10%, the distance from the airbridge provided on the control line to the branch point of the controlline is preferably equal to or longer than 1/20 of the wavelength of thecontrol signal (i.e., the value on the horizontal axis in FIG. 20 ispreferably equal to or higher than 0.05). Based on the above-describedfacts, it is considered as follows. When only one air bridge is providedon the control line, the distance between the air bridge provided on thecontrol line and the branch point of the control line is preferably aslong as possible in order to improve the crosstalk reduction effect. Forexample, the distance from the air bridge provided on the control lineto the branch point of the control line is preferably equal to or longerthan 1/20 of the wavelength of the high-frequency control signal (acontrol signal having a frequency twice the operating frequency of thequantum bit) input from the control line on the chip. In other words,the distance from the air bridge to the branch point on the control lineis preferably equal to or longer than 1/20 of the wavelength of thecontrol signal. More preferably, the distance from the air bridgeprovided on the control line to the branch point of the control line ispreferably equal to or longer than ⅒ of the wavelength. Note that, inthe second example embodiment, the number of air bridges provided on thecontrol line may be two or more. Note that the above-described positionof the air bridge provided on the control line may be adopted in thefirst example embodiment.

First Modified Example of Second Example Embodiment

In the second example embodiment, the first and second branch lines 2041and 2042 have shapes identical to each other, and have inductances equalto each other. However, the same advantageous effects as those in thesecond example embodiment can be obtained even when the shapes of thefirst and second branch lines 2041 and 2042 are not identical to eachother. In other words, even when the first and second branch lines 2041and 2042 do not have inductances equal to each other, it is possible tomake two types of magnetic fluxes having magnitudes equal to each otherand directions opposite to each other pass through the superconductingloop 209 by the control current (the control signal) flowing through thecontrol line 204. That is, advantageous effects similar to those in thesecond example embodiment can be obtained by other configurations. As anexample of such a modified example of the second example embodiment,assume a case where, for example, the air bridges 207 a and 207 b areprovided so that they are at equal distances from the branch point 208of the control line 204, but the line width of the second branch line2042 is larger than that of the first branch line 2041. That is, assumea case where the inductance L2 of the second branch line 2042 is smallerthan the inductance L1 of the first branch line 2041. In this case, thecontrol current I0 input from the control line 204 is divided into acurrent I1 flowing through the first branch line 2041 and a current I2flowing through the second branch line 2042, and the current I0 isdivided according to the ratio between the reciprocals of theinductances of these branch lines. That is, a relation I1:I2 = L2:L1holds. Therefore, a relation I1L1 = I2L2 holds. Therefore, a magneticflux 11L1 (the product of I1 and L1) generated by the current I1 flowingthrough the first branch line 2041 (the inductance L1) and a magneticflux I2L2 (the product of I2 and L2) generated by the current I2 flowingthrough the second branch line 2042 (the inductance L2) are equal toeach other irrespective of the values of the inductances L1 and L2. Notethat since the air bridges 207 a and 207 b are disposed in the placewhere the first branch line 2041 is connected to the GND and the secondbranch line 2042 is connected to ground, respectively, i.e., disposed atthe ends of the respective branch lines, the magnetic flux that isgenerated by the control current and passes through the inside of thesuperconducting loop 209 consists of the magnetic flux 11L1 and themagnetic flux I2L2. Therefore, the magnetic flux generated by thecurrent I1 in the area inside the superconducting loop 209 (MagneticFlux = Current × Inductance) and the magnetic flux generated by thecurrent I2 have magnitudes equal to each other and directions oppositeto each other, so that they cancel each other. Therefore, although thereis the property that the magnetic flux that passes through the inside ofthe superconducting loop 209 must be conserved as described above, themagnetic flux in the area inside the superconducting loop 209 isconserved at zero (i.e., remains at zero). Therefore, when the controlcurrent is input, no shielding current caused by the control current isgenerated in the superconducting loop 209, so that it does not affectthe setting of the resonance frequency.

Second Modified Example of Second Example Embodiment

FIG. 21 is a layout of a superconducting circuit according to a secondmodified example. Further, FIG. 22 shows an equivalent circuit of thesuperconducting circuit according to the second modified example.Similarly to the above-described example embodiment, the superconductingcircuit according to this modified example can be used as asuperconducting quantum bit. Note that, similarly to the description ofthe above-described example embodiment, a configuration of one quantumbit is described in detail with reference to the drawings, and thedescription of the other quantum bit(s) having a similar configurationis omitted. Further, descriptions of configurations similar to those inthe second example embodiment will be omitted as appropriate, anddifferences therefrom will be described in detail. In theabove-described example embodiment, the end side of the control line 204separates into two branches, and the two ends of the control line 204are connected to parts of the GND plane 206 located on both sides of thecontrol line 204, respectively. In contrast, in this modified example,the end side of the control line 204 does not separate into branches,and the end of the control line 204 is connected to only one of parts ofthe GND plane 206 located on both sides of the control line 204. Thatis, in this modified example, the control line 204 is a single linehaving no branch. Note that the end side of the control line 204 iswired (i.e., routed) along the SQUID 202 so that the control line 204magnetically couples with the SQUID 202. In the example shown in thedrawing, the control line 204 is an L-shaped line, and specifically isconfigured as follows. That is, the control line 204 shown in FIG. 21 isan L-shaped line including a part extending along the SQUID 202 in afirst direction (the up/down direction in the drawing) and a partextending in a second direction (the left/right direction in thedrawing). That is, the control line 204 shown in FIG. 21 is bent at 90degrees in the vicinity of the SQUID 202, and the part of the controlline 204 extending in the second direction extends in a directionreceding from the SQUID 202.

In the superconducting quantum bit according to this modified example, asuperconducting loop 209 is formed by air bridges 207 a, 207 b and 207 cso as to surround the outside of the SQUID 202. That is, in thismodified example, the superconducting loop 209 is a circuit made of asuperconductor using the GND plane 206 and the air bridges 207 a, 207 band 207 c. In the configuration shown in FIG. 21 , the air bridges 207 aand 207 b are provided in the vicinity of the SQUID 202 as in the caseof the first or second example embodiment. The air bridge 207 a is aconnection circuit made of a superconductor that connects parts of theGND plane 206 located on both sides of the λ/4 line 203 a to each other,and the air bridge 207 b is a connection circuit made of asuperconductor that connects parts of the GND plane 206 located on bothsides of the λ/4 line 203 b to each other. Further, the air bridge 207 cis a connection circuit made of a superconductor that connects parts ofthe GND plane 206 located on both sides of the control line 204 to eachother.

In this modified example, the air bridges 207 a and 207 b are alsoprovided, on the λ/4 lines 203 a and 203 b, only at places that are asclose as possible to the connection parts with the SQUID 202 as in thecase of the first and second example embodiments. Therefore, thismodified example provides an advantageous effect similar to thatdescribed in the first and second example embodiments, i.e., theadvantageous effect that the high-frequency crosstalk is reduced whilepreventing the Q-value of the quantum bit from deteriorating.

Further, this modified example has also a configuration in which thesuperconducting loop 209 surrounds the outside of the SQUID 202, andtherefore provides an advantageous effect similar to that described inthe second example embodiment, i.e., the advantageous effect that thecrosstalk that is caused as a current flows through the GND plane isreduced by the effect of the shielding current.

Note that although the superconducting loop circuit using the first andsecond branch lines 2041 and 2042 is formed in the second exampleembodiment, such a superconducting loop circuit is not formed in thismodified example. Theoretically, even when a superconducting loopcircuit using the first and second branch lines 2041 and 2042 is formed,no shielding current is generated due to the control current flowingthrough the control line 204 as described above. However, if a shieldingcurrent caused by the control current is generated for some reason, amagnetic flux caused by the shielding current could significantly affectthe SQUID 202. This is because there is a large mutual inductancebetween the first branch line 2041, which is formed in a linear shape,and the SQUID 202. If the magnetic flux caused by the aforementionedshielding current affects the SQUID 202, it hinders the setting of theresonance frequency to an intended value. Further, if the magnetic fluxgenerated by the control current flowing through the second branch line2042 passes through the loop of the SQUID 202 for some reason, it alsohinders the setting of the resonance frequency to an intended value. Tocope with this, in this modified example, the superconducting loop 209surrounding the SQUID 202 does not use the first and second branch lines2041 and 2042. That is, as described above, the superconducting loop 209formed by the GND plane 206 and the air bridges 207 a, 207 b and 207 csurrounds the SQUID 202. Therefore, as compared to the configurationshown in the second example embodiment, it is possible to prevent thesetting of the resonance frequency to an intended value from beinghindered. Further, since the control line 204 does not separate intobranches, it is possible to increase the part of the control currentthat contributes to applying the magnetic flux to the SQUID 202 ascompared to the case where the control line 204 separates into branches.

Third Example Embodiment

FIG. 23 is a layout of a superconducting circuit according to a thirdexample embodiment. Further, FIG. 24 shows an equivalent circuit of thesuperconducting circuit according to the third example embodiment.Similarly to the above-described example embodiments, thesuperconducting circuit according to the third example embodiment is asuperconducting quantum bit. In the description of this exampleembodiment, similarly to the descriptions of the above-described exampleembodiments, a configuration of one quantum bit will be described indetail with reference to the drawings, and the description of the otherquantum bit(s) having a similar configuration is omitted. Note that thisalso applies to the descriptions of other example embodiments and thelike described later, unless otherwise specified. The equivalent circuitshown in FIG. 24 is similar to the equivalent circuit of the firstquantum bit 1 or the second quantum bit 2 shown in FIG. 8 , except thatthe configuration of the control line is different. Specifically, unlikethe superconducting quantum bits of the first and second exampleembodiments, the control line 104 does not separate into branches in thesuperconducting quantum bit according to the third example embodiment.Further, a superconducting loop 109 is formed by air bridges 107 a, 107b and 107 c so as to surround the outside of the SQUID 102 in thesuperconducting quantum bit according to the third example embodiment.That is, in this example embodiment, the superconducting loop 109 is acircuit made of a superconductor using the GND plane 106 and the airbridges 107 a, 107 b and 107 c. Further, a control line 104 has such ashape that it enters the superconducting loop 109 from the outsidethereof, is folded back inside the superconducting loop 109, and thengoes out from the superconducting loop 109 again. That is, in thisexample embodiment, the control line 104 is wired (i.e., routed) in aU-shape so that it is folded back in the vicinity of the SQUID 102. Inthis example embodiment, the air bridges 107 a and 107 b are provided inthe vicinity of the SQUID 102 as in the case of the first or secondexample embodiment. In this example embodiment, the air bridge 107 cconnects the GND plane 106 across the control line 104 as in the case ofthe first and second example embodiments. However, in this exampleembodiment, the air bridge 107 c is a connection circuit made of asuperconductor that connects parts of the GND plane 106 located on bothsides of the two straight sections, i.e., the outward and returningsections, of the U-shaped control line 104 to each other.

Note that the positional relationship among the SQUID 102, the λ/4 lines103 a and 103 b, and the control line 104 is, for example, as shown inFIG. 23 and will be described hereinafter. The λ/4 lines 103 a and 103 band the SQUID 102 are arranged in a first direction (the up/downdirection in the drawing) in the vicinity of the SQUID 102. Further, thecontrol line 104 extends in a second direction (the left/right directionin the drawing) in the vicinity of the SQUID 102, and is folded back inthe vicinity of the SQUID 102. That is, the control line 104 is wired(i.e., routed) on the side of the folded-back part opposite to the sidethereof on which the SQUID 102 is located.

In the third example embodiment, the air bridges 107 a and 107 b arealso provided, on the λ/4 lines 103 a and 103 b, only at places that areas close as possible to the connection parts with the SQUID 102 as inthe case of the first and second example embodiments. Therefore, thethird example embodiment also provides an advantageous effect similar tothat described in the first and second example embodiments, i.e., theadvantageous effect that the high-frequency crosstalk is reduced whilepreventing the Q-value of the quantum bit from deteriorating.

Further, the third example embodiment has also a configuration in whichthe superconducting loop 109 surrounds the outside of the SQUID 102, andtherefore provides an advantageous effect similar to that described inthe second example embodiment, i.e., the advantageous effect that thecrosstalk that is caused as a current flows through the GND plane isreduced by the effect of the shielding current. Further, as shown inFIG. 23 , when the control current I0 is supplied from the control line104 in order to control the quantum bit, the magnetic fluxes generatedon the right and left sides of the control line 104 by the current I0have magnitudes equal to each other and directions opposite to eachother. Therefore, it is possible to make the magnetic fluxes G0 a and G0b generated inside the superconducting loop 109 by the current I0 zeroor very small in total. Therefore, it is possible to make the shieldingcurrent that is generated in the superconducting loop when the controlcurrent I0 is input from the control line 104 zero or very small.Accordingly, the setting of the resonance frequency is not affected.

Fourth Example Embodiment

FIG. 25 shows a layout of a superconducting circuit according to afourth example embodiment. Further, FIG. 26 shows an equivalent circuitof the superconducting circuit according to the fourth exampleembodiment. Similarly to the above-described example embodiments, thesuperconducting circuit according to the fourth example embodiment is asuperconducting quantum bit. In the description of this exampleembodiment, similarly to the descriptions of the above-described exampleembodiments, a configuration of one quantum bit will be described indetail with reference to the drawings, and the description of the otherquantum bit(s) having a similar configuration is omitted. The equivalentcircuit shown in FIG. 26 is similar to the equivalent circuit of thefirst quantum bit 1 or the second quantum bit 2 shown in FIG. 8 , exceptthat the configuration of the control line is different. Specifically,unlike the superconducting quantum bits of the first and second exampleembodiments, the control line 104 does not separate into branches in thesuperconducting quantum bit according to the fourth example embodiment.Further, a superconducting loop 109 is formed by air bridges 107 a, 107b, 107 c and 107 d so as to surround the outside of the SQUID 102 in thesuperconducting quantum bit according to the fourth example embodiment.That is, in this example embodiment, the superconducting loop 109 is acircuit made of a superconductor using the GND plane 106 and the airbridges 107 a, 107 b, 107 c and 107 d. Further, a control line 104 hassuch a shape that it enters the superconducting loop 109 from theoutside thereof, and then goes out from the superconducting loop 109again. That is, in this example embodiment, the control line 104 iswired (i.e., routed) in a straight line and intersects with one of thetwo transmission lines (the λ/4 lines 103 a and 103 b) connected to theSQUID 102 in a three-dimensional manner (i.e., like an overpass). Morespecifically, as shown in FIG. 25 , an air bridge 107 e is provided inthe middle of the control line 104 to cross over (i.e., cross above) theλ/4 line 103 b. That is, the control line 104 and the λ/4 line 103 bintersect with each other in a three-dimensional manner by the airbridge 107 e (i.e., like an overpass). In this example embodiment, theair bridges 107 a and 107 b are provided in the vicinity of the SQUID102 as in the case of the first and second example embodiments. In thisexample embodiment, the air bridges 107 c and 107 d connect parts of theGND plane 106 located on both sides of the control line 104 to eachother by crossing over (i.e., crossing above) the control line 104 as inthe case of the first and second example embodiments. The air bridges107 c and 107 d are provided on both sides of the place where thecontrol line 104 and the λ/4 line 103 b intersect with each other in athree-dimensional manner.

Note that the positional relationship among the SQUID 102, the λ/4 lines103 a and 103 b, and the control line 104 is, for example, as shown inFIG. 25 and will be described hereinafter. The λ/4 lines 103 a and 103 band the SQUID 102 are arranged in a first direction (the up/downdirection in the drawing) in the vicinity of the SQUID 102. Further, thecontrol line 104 extends in a second direction (the left/right directionin the drawing) in the vicinity of the SQUID 102 while intersecting theλ/4 line 103 b in a three-dimensional manner. In other words, thecontrol line 104 is wired so as to cross over the transmission line in adirection intersecting the direction in which the transmission line andthe SQUID are arranged.

In the fourth example embodiment, the air bridges 107 a and 107 b arealso provided, on the λ/4 lines 103 a and 103 b, only at places that areas close as possible to the connection parts with the SQUID 102 as inthe case of the first, second and third example embodiments. Therefore,the fourth example embodiment provides an advantageous effect similar tothat described in the first, second and third example embodiments, i.e.,the advantageous effect that the high-frequency crosstalk is reducedwhile preventing the Q-value of the quantum bit from deteriorating.

Further, the fourth example embodiment has also a configuration in whichthe superconducting loop 109 surrounds the outside of the SQUID 102, andtherefore provides an advantageous effect similar to that described inthe second and third example embodiments, i.e., the advantageous effectthat the crosstalk that is caused as a current flows through the GNDplane is reduced by the effect of the shielding current. Further, asshown in FIG. 25 , when the control current I0 is supplied from thecontrol line 104 in order to control the quantum bit, the magneticfluxes generated on the right and left sides of the control line 104 bythe current I0 have magnitudes equal to each other and directionsopposite to each other. Therefore, it is possible to make the magneticfluxes G0 a and G0 b generated inside the superconducting loop 109 bythe current I0 zero or very small in total. Therefore, it is possible tomake the shielding current that is generated in the superconducting loopwhen the control current I0 is input from the control line 104 zero orvery small. Accordingly, the setting of the resonance frequency is notaffected.

Other Configuration

In the first, second, third and fourth example embodiments, an airbridge is used as a connection circuit for electrically short-circuitingparts of the GND plane located on both sides of core lines of λ/4 lineto each other, and any type of conductive material can be used as thematerial for such an air bridge. However, in order to make thepotentials of the parts of the GND plane located on both sides of thecore line as equal as possible, the conductive material preferably hasan electrical resistance as small as possible. Further, most preferably,the conductive material is a material that becomes a superconductor at atemperature at which the quantum circuit is operated (about 10 mK). Notethat since a superconducting loop circuit made of a superconductor isrequired to achieve the DC crosstalk reduction effect using a shieldingcurrent, the air bridge(s) and the GND plane(s) that constitute thesuperconducting loop circuit need to be made of a superconductor.Examples of the materials that become a superconductor at thetemperature at which the quantum circuit is operated include aluminum(Al), tantalum (Ta), niobium (Nb), and alloys containing any of them.Further, the GNDs on both sides of the λ/4 line or the control line maybe electrically short-circuited by using, instead of the air bridge, abonding wire. Any type of conductor can be used as the material for sucha bonding wire. However, the material for such a bonding wire preferablyhas an electrical resistance as small as possible, and most preferably,it is a material that becomes a superconductor at the temperature atwhich the quantum circuit is operated. Even when a bonding wire is used,the bonding wire must be made of a superconductor in order to achievethe DC crosstalk reduction effect using a shielding current. Examples ofthe materials that become a superconductor at the temperature at whichthe quantum circuit is operated include aluminum (Al). Further, insteadof using the air bridge, the below-described connection circuit may beused. That is, a structure in which a TSV (Through Silicon Via) isformed in each of parts of the GND plane located on both sides of thecore line of the λ/4 line, and wiring lines for electrically connectingthese TSVs to each other are formed on the rear surface of the chip maybe used as a connection circuit. The connection circuit that intersectsthe core line of the λ/4 line in a three-dimensional manner withoutbeing in contact with the core line of the λ/4 line can also be realized(i.e., formed) by using the above-described structure. Any type ofconductive material can be used as the material for the TSVs and thewiring lines provided on the rear surface of the chip. However, in orderto make the potentials of the parts of the GND planes located on bothsides of the core line as equal as possible, the conductive materialpreferably has an electrical resistance as small as possible. Further,most preferably, the conductive material is a material that becomes asuperconductor at the temperature at which the quantum circuit isoperated (about 10 mK). Note that since a superconducting loop circuitmade of a superconductor is required to achieve the DC crosstalkreduction effect using a shielding current, the TSVs, the wiring linesprovided on the rear surface of the chip, and the GND plane(s) thatconstitute the superconducting loop circuit need to be made of asuperconductor. Examples of the materials that become a superconductorat the temperature at which the quantum circuit is operated includealuminum (Al), tantalum (Ta), niobium (Nb), and alloys containing any ofthem. Further, in a configuration in which a chip including a quantumcircuit formed therein is connected to a substrate such as an interposerby using a flip-chip connecting technique (hereinafter also referred toas being flip-chip connected), instead of using the air bridges, bumpsfor connecting the chip to the substrate and wiring lines provided onthe substrate may be used. That is, the parts of the GND plane locatedon both sides of the λ/4 line or the control line on the chip areelectrically short-circuited to each other by bumps and wiring linesprovided on the substrate. Even in this case, any type of conductivematerial can be used as the material for such bumps and wiring linesprovided on the substrate. However, the material for such bumps andwiring lines preferably has an electrical resistance as small aspossible, and most preferably, it is a material that becomes asuperconductor at the temperature at which the quantum circuit isoperated. For the bumps, examples of the materials that become asuperconductor at the temperature at which the quantum circuit isoperated include indium (In). Further, for the wiling lines in theinterposer, examples of such materials include niobium (Nb) and aluminum(Al). Even in this case, the bumps and the wiring lines provided on thesubstrate must be a superconductor in order to achieve the DC crosstalkreduction effect using a shielding current.

Further, the first, second, third and fourth example embodiments havebeen described by using a 2-bit distributed constant-type quantumcircuit as an example of the quantum circuit in which a plurality ofquantum bits are integrated. However, the number of integrated quantumbits does not have to be two. That is, the above-described exampleembodiments can be applied to a quantum circuit in which three or moredistributed constant-type quantum bits are integrated, and by doing so,similar advantageous effects can be obtained.

Further, although the distributed constant-type quantum bits have beendescribed so far, the idea of reducing crosstalk that is caused as acurrent flows through a GND plane by the shielding effect of asuperconducting loop can also be applied to lumped constant-type quantumbits. A lumped constant-type quantum bit will be described hereinafter.

FIG. 27 shows an example of an equivalent circuit of a lumpedconstant-type quantum bit 2000. A lumped constant-type quantum bit 2000is a loop circuit in which each of the terminals of a SQUID 2001 isconnected to a respective one of the terminals of a capacitor 2003 by asuperconducting wiring line. In other words, the input and outputterminals of the SQUID 2001 are shunted by the capacitor 2003. That is,it can be said that, by connecting the capacitor 2003 and the SQUID 2001in a ring shape (i.e., in a circular fashion), a loop circuit in whichthe SQUID 2001 is incorporated into the loop line is formed. The SQUID2001 is a loop circuit including two Josephson junctions 2002 a and 2002b. That is, the SQUID 2001 is formed by connecting the two Josephsonjunctions 2002 a and 2002 b in a ring shape. One of the terminals of theSQUID 2001 may be connected to the ground. A control line 2004 ismagnetically coupled with the SQUID 2001. In other words, the controlline 2004 and the SQUID 2001 magnetically couple with each other bytheir mutual inductance in a noncontact manner.

In the distributed constant-type quantum bit shown in FIG. 2 , aresonator is formed by using the SQUID and the λ/4 lines. As shown inFIG. 27 , the lumped constant-type quantum bit 2000 differs from thedistributed constant-type quantum bit because an LC resonant circuit isformed by the effective inductance of the SQUID 2001 and the capacitor2003 in the lumped constant-type quantum bit 2000. A distributedconstant-type quantum bit such as the one shown in FIG. 2 has a sizeroughly equal to the length of the wavelength corresponding to theoperating frequency of the quantum bit, so that the size of the quantumbit is very large. In contrast, the lumped constant-type quantum bit2000 such as the one shown in FIG. 27 does not use any distributedconstant line, so that the quantum bit can be realized (i.e., formed) bya circuit that is very small compared to the wavelength corresponding tothe operating frequency of the quantum bit 2000. Therefore, it has anadvantage that when a large number of quantum bits 2000 are integrated,they can be integrated in a small area.

The way of operating the lumped constant-type quantum bit 2000 issimilar to that for the distributed constant-type quantum bit shown inFIG. 2 . That is, it is possible to set the resonance frequency of thequantum bit 2000 by inputting a DC control signal from the control line2004. In a state in which a DC control signal for setting the resonancefrequency to a certain frequency is being input to the control line2004, it is possible to make the quantum bit 2000 oscillate by furtherinputting a control signal having a frequency twice the set resonancefrequency to the control line 2004. The operating frequency (the setresonance frequency) of the quantum bit 2000 is, for example, about 10GHz. Therefore, when the quantum bit 2000 is operated, a signal in whicha DC control signal and a high-frequency control signal having afrequency of about 20 GHz are superimposed is input thereto from thecontrol line 2004. Note that, as described above, the lumpedconstant-type quantum bit oscillates by the control signal from thecontrol line. Therefore, a configuration including a lumpedconstant-type quantum bit may also be referred to as an oscillator.

FIG. 28 shows an example of a layout of the lumped constant-type quantumbit 2000 shown in FIG. 27 . In this example, a quantum bit 2000 having acoplanar waveguide structure is realized (i.e., formed) by forming athin film of a superconducting material (e.g., niobium or aluminum) on asilicon substrate. As shown in FIG. 28 , in the quantum bit 2000, across-shaped electrode (also referred to as a conductive member) 2005 isformed inside a cross-shaped area formed in a GND plane 2006 (i.e., across-shaped space formed by removing a cross-shaped piece from the GNDplane 2006). That is, the GND plane 2006 is disposed around theelectrode 2005 so as to surround the electrode 2005. Note that the GNDplane 2006 and the electrode 2005 are apart from each other, and thereis a gap therebetween. One end of the electrode 2005 is connected to theGND plane 2006 by using two narrow electrodes, and a Josephson junction2002 a is provided in the middle of one of these two narrow electrodes,and a Josephson junction 2002 b is provided in the middle of the othernarrow electrode. By the above-described configuration, a SQUID 2001 isformed by the electrode 2005, the GND plane 2006, and the two Josephsonjunctions 2002 a and 2002 b. That is, in the SQUID 2001, the electrode2005 and the GND plane 2006 are used to connect the two Josephsonjunctions 2002 a and 2002 b, which form the SQUID 2001, in a loop. Asdescribed above, one end of the SQUID 2001 is connected to the electrode2005 and the other end thereof is connected to the GND plane 2006. Notethat it can be said that the SQUID 2001 is disposed between theelectrode 2005 and the GND plane 2006. As described above, in thequantum bit 2000, as shown in FIG. 28 , the SQUID 2001 is connected toone of the four ends, i.e., outwardly protruding parts of thecross-shaped electrode 2005 (i.e., the tip of one of the four arms ofthe cross-shaped electrode 2005), in such a manner that the SQUID 2001serves as a bridge between the electrode 2005 and the GND plane 2006.Since there is a gap between the cross-shaped electrode 2005 and the GNDplane, a capacitor 2003 is formed between the electrode 2005 and the GNDplane 2006. Further, the control line 2004 is disposed in a straightline near the SQUID 2001. That is, in FIG. 28 , a horizontally-longelectrode disposed below the cross-shaped electrode 2005 is a controlline 2004. When a current is fed to the control line 2004, a part of themagnetic flux generated by the current flowing through the control line2004 passes through the loop of the SQUID 2001, making it possible tocontrol the effective inductance of the SQUID 2001 and/or to make thequantum bit 2000 oscillate.

The layout shown in FIG. 28 is susceptible to the crosstalk describedabove, especially to the crosstalk that is caused as a current flowsthrough the GND plane. In a chip in which a plurality of quantum bits2000 are integrated, the aforementioned crosstalk could occur because,for example, when a DC control current is input to a given quantum bit2000, the SQUID 2001 of another quantum bit 2000 senses (i.e., isaffected by) a magnetic field that is generated when the DC controlcurrent flows through the GND plane after flowing through the controlline thereof. A method similar to the above-described method can beapplied in order to reduce the effect of such crosstalk. An exampleembodiment for reducing the effect of crosstalk in a lumpedconstant-type quantum bit will be described hereinafter.

Fifth Example Embodiment

FIG. 29 shows a layout of a quantum bit according to a fifth exampleembodiment. Differences from the configuration shown in FIG. 28 will bedescribed hereinafter, and descriptions of similar components/structureswill be omitted as appropriate. Since the equivalent circuit of thelumped constant-type quantum bit 2000 according to this exampleembodiment is similar to that shown in FIG. 27 , the layout shown inFIG. 28 will be described. In this example embodiment, a quantum bit2000 having a coplanar waveguide structure is also shown. Therefore, asshown in FIG. 29 , the electrode 2005 and the control line 2004 areformed as a coplanar waveguide, and a GND plane 2006 made of asuperconductor is located around the line that is formed as the coplanarwaveguide. In this example embodiment, as shown in FIG. 29 , in thequantum bit 2000, a cross-shaped electrode (also referred to as aconductive member) 2005 is also formed inside a cross-shaped area formedin the GND plane 2006 (i.e., a cross-shaped space formed by removing across-shaped piece from the GND plane 2006). That is, the GND plane 2006is disposed around the electrode 2005 so as to surround the electrode2005. Further, there is a gap between the GND plane 2006 and theelectrode 2005, and a capacitor 2003 is formed between the electrode2005 and the GND plane 2006 by this gap. Further, in this exampleembodiment, in the quantum bit 2000, the SQUID 2001 is connected to oneof the four ends, i.e., outwardly protruding parts of the cross-shapedelectrode 2005 (i.e., the tip of one of the four arms of thecross-shaped electrode 2005), in such a manner that the SQUID 2001serves as a bridge between the electrode 2005 and the GND plane 2006.However, while one end of the SQUID 2001 is directly connected to theelectrode 2005, the other end thereof is connected to the GND plane 2006through one narrow electrode 2008. Note that the electrode 2008 may alsobe referred to as a connection conductive member or a conductive line.In the example shown in FIG. 29 , the electrode 2005, the SQUID 2001,and the electrode 2008 are arranged in a first direction (the up/downdirection in the drawing). In other words, the SQUID 2001 and theelectrode 2008 are arranged in the direction in which the one of thefour arms of the cross-shaped electrode 2005 to which the SQUID 2001 isconnected extends. Note that, in this example embodiment, the SQUID 2001is also formed by a Josephson junction 2002 a provided in the middle ofone of the two narrow electrodes and a Josephson junction 2002 bprovided in the middle of the other narrow electrode. That is, in thisexample embodiment, in the SQUID 2001, the electrodes 2005 and 2008 areused to connect the two Josephson junctions 2002 a and 2002 b, whichform the SQUID 2001, in a loop. Therefore, as described above, one endof the SQUID 2001 is connected to the electrode 2005, and the other endthereof is connected to the GND plane 2006 through the electrode 2008.Note that it can be said that the SQUID 2001 is disposed between theelectrode 2005 and the GND plane 2006.

As shown in FIG. 29 , in this example embodiment, the control line 2004is disposed next to the SQUID 2001, and the tip of the control line 2004separates into a first branch line 20041 and a second branch line 20042at a branch point 2108. Further, the first branch line 20041 is disposednear the SQUID 2001 so that the first branch line 20041 and the SQUID2001 magnetically couple with each other. Meanwhile, the second branchline 20042 is disposed far from the SQUID 2001 in order to prevent thesecond branch line 20042 and the SQUID 2001 magnetically coupling witheach other. Specifically, in order to make the first branch line 20041and the SQUID 2001 magnetically couple with each other while preventingthe second branch line 20042 and the SQUID 2001 from magnetically couplewith each other, these branch lines are wired (i.e., routed) as follows.That is, the first branch line 20041 is wired along the SQUID 2001, andthe second branch line 20042 is wired along the electrode 2008 in thedirection opposite to the direction of the first branch line 20041. Thefirst and second branch lines 20041 and 20042 are both connected to theGND plane 2006.

The control line 2004 is a T-shaped line, and the first and secondbranch lines 20041 and 20042, which are separated from each other at thebranch point 2108, are arranged in a straight line. Note that thepositional relationship among the SQUID 2001, the electrode 2005, andthe control line 2004 is, for example, as shown in FIG. 29 and will bedescribed hereinafter. As described above, the electrode 2005 and theSQUID 2001 are arranged in a first direction (the up/down direction inthe drawing) in the vicinity of the SQUID 2001. Further, the first andsecond branch lines 20041 and 20042 are also wired in this firstdirection (the up/down direction in the drawing). Note that thenon-branched part of the control line 204 (i.e., the part of the controlline 2004 other than the first and second branch lines 20041 and 20042)extends in a second direction (the left/right direction in the drawing)in the vicinity of the SQUID 2001, and extend from the branch point 2108so as to recede from the SQUID 2001. That is, the non-branched part ofthe control line 2004 is wired on the side of the branch point 2108opposite to the side thereof on which the SQUID 2001 is located. Whilethe first branch line 20041 is located so as to be opposed to the SQUID2001, the second branch line 20042 is located so as to be not opposed tothe SQUID 2001.

Further, in this example embodiment, an air bridge 2007 a is provided inthe vicinity of the terminal of the SQUID 2001 on the side thereof onwhich the electrode 2005 is located. The air bridge 2007 a is aconnection circuit made of a superconductor that connects parts of theGND plane 2006 located on both sides of the connection part between theSQUID 2001 and the electrode 2005 to each other. In the configurationshown in FIG. 29 , the air bridge 2007 a connects the parts of the GNDplane 2006 located on both sides of the connection part between theelectrode 2005 and the SQUID 2001 to each other by crossing over (i.e.,crossing above) the vicinity of this connection part. More specifically,the air bridge 2007 a connects parts of the GND plane 2006 located onboth sides of the end of the electrode 2005 connected to the SQUID 2001to each other by crossing over (i.e., crossing above) this end of theelectrode 2005. In this way, in this example embodiment, asuperconducting loop 2009 is formed by the air bridge 2007 a, the GNDplane 2006, and the first and second branch lines 20041 and 20042 so asto surround the SQUID 2001. Specifically, this superconducting loop 2009surrounds the SQUID 2001 and the narrow electrode 2008. All of the airbridge 2007 a, the GND plane 2006, and the first and second branch lines20041 and 20042, which constitute the superconducting loop 2009, aremade of a superconductor. The first and second branch lines 20041 and20042, which constitute the superconducting loop 2009, have shapesidentical to each other. As described above, this example embodimentincludes the superconducting loop 2009 surrounding the SQUID 2001, sothat it provides an advantageous effect that the effect of the crosstalkcan be reduced. Further, in the superconducting loop 2009, the first andsecond branch lines 20041 and 20042 have shapes identical to each other.Therefore, a current input from the control line 2004 is divided intothose flowing through the first and second branch lines 20041 and 20042so that the divided currents have amounts equal to each other anddirections opposite to each other. Therefore, the occurrence of ashielding current in the superconducting loop 2009, which wouldotherwise be caused by the input of the control current to the controlline 2004, is suppressed, and the resonance frequency is prevented frombeing set (i.e., changed) to an unintended frequency.

Note that, as shown in FIG. 30 , an air bridge 2007 b that connectsparts of the GND plane 2006 located on both sides of the core line ofthe non-branched part of the control line 2004 to each other may befurther added.

Modified Example of Fifth Example Embodiment

FIG. 31 is a layout of a lumped constant-type quantum bit according to amodified example of the fifth example embodiment. Differences from thefifth example embodiment will be described hereinafter in detail. In thefifth example embodiment, the end side of the control line 2004separates into two branches, and the two ends of the control line 2004are connected to the parts of the GND plane 2006 located on both sidesof the control line 2004, respectively. In contrast, in this modifiedexample, the end side of the control line 2004 does not separate intobranches, and the end of the control line 2004 is connected to only oneof parts of the GND plane 2006 located on both sides of the control line2004. That is, in this modified example, the control line 2004 is asingle line having no branch. Note that the end side of the control line2004 is wired (i.e., routed) along the SQUID 2001 so that the controlline 2004 magnetically couples with the SQUID 2001. In the example shownin the drawing, the control line 2004 is an L-shaped line, andspecifically is configured as follows. That is, the control line 2004shown in FIG. 31 is an L-shaped line including a part extending alongthe SQUID 2001 in a first direction (the up/down direction in thedrawing) and a part extending in a second direction (the left/rightdirection in the drawing). That is, the control line 2004 shown in FIG.31 is bent at 90 degrees in the vicinity of the SQUID 2001, and the partof the control line 2004 extending in the second direction extends in adirection receding from the SQUID 2001. Note that although the controlline 2004 has the L-shape in the example shown in FIG. 31 , the controlline 2004 may be a straight line extending in the first direction (theup/down direction in the drawing).

In the superconducting quantum bit according to this modified example, asuperconducting loop 2009 is formed by air bridges 2007 a and 2007 b soas to surround the outside of the SQUID 2001. That is, in this modifiedexample, the superconducting loop 2009 is a circuit made of asuperconductor using the GND plane 2006 and the air bridges 2007 a and2007 b. In the configuration shown in FIG. 31 , the air bridge 2007 a isprovided in the vicinity of the terminal of the SQUID 2001 on the sidethereof on which the electrode 2005 is located as in the case of thefifth example embodiment. The air bridge 2007 a is a connection circuitmade of a superconductor that connects parts of the GND plane 2006located on both sides of the connection part between the SQUID 2001 andthe electrode 2005 to each other. Further, the air bridge 2007 b is aconnection circuit made of a superconductor that connects parts of theGND plane 2006 located on both sides of the control line 2004 to eachother.

This modified example also includes the superconducting loop 2009surrounding the SQUID 2001, so that it provides an advantageous effectthat the effect of the crosstalk that is caused as a current flowsthrough the GND plane can be reduced.

Note that although the superconducting loop circuit using the first andsecond branch lines 20041 and 20042 is formed in the fifth exampleembodiment, such a superconducting loop circuit is not formed in thismodified example. Therefore, as described in the description of thesecond modified example of the second example embodiment, it is possibleto prevent the setting of the resonance frequency to an intended valuefrom being hindered. Further, since the control line 2004 does notseparate into branches, it is possible to increase the part of thecontrol current that contributes to applying the magnetic flux to theSQUID 2001 as compared to the case where the control line 2004 separatesinto branches.

Sixth Example Embodiment

Next, another example embodiment for reducing the effect of crosstalk ina lumped constant-type quantum bit will be described. FIG. 32 shows alayout of a lumped constant-type quantum bit according to a sixthexample embodiment. Differences from the fifth example embodiment willbe described hereinafter in detail. As shown in FIG. 32 , unlike thefifth example embodiment, the control line 2004 does not separate intobranches in this example embodiment. Further, in this exampleembodiment, a superconducting loop 2009 is formed by air bridges 2007 aand 2007 b to surround the outside of the SQUID 2001. That is, in thisexample embodiment, the superconducting loop 2009 is a circuit made of asuperconductor using the GND plane 2006 and the air bridges 2007 a and2007 b. Further, a control line 2004 has such a shape that it enters thesuperconductor loop 2009 from the outside thereof, is folded back insidethe superconductor loop 2009, and then goes out from the superconductorloop 2009 again. That is, in this example embodiment, the control line2004 is wired (i.e., routed) in a U-shape so that it is folded back inthe vicinity of the SQUID 2001. In this example embodiment, the airbridge 2007 a is provided in the vicinity of the terminal of the SQUID2001 on the side thereof on which the electrode 2005 is located as inthe case of the fifth example embodiment. The air bridge 2007 b connectsthe GND plane 106 across the control line 2004. Specifically, the airbridge 2007 b is a connection circuit made of a superconductor thatconnects parts of the GND plane 2006 located on both sides of the twostraight sections, i.e., the outward and returning sections, of theU-shaped control lines 104 to each other.

Note that the positional relationship among the SQUID 2001, theelectrode 2005, and the control line 2004 is, for example, as shown inFIG. 32 and will be described hereinafter. The electrode 2005 and theSQUID 2001 are arranged in a first direction (the up/down direction inthe drawing) in the vicinity of the SQUID 2001. Further, the controlline 2004 extends in a second direction (the left/right direction in thedrawing) in the vicinity of the SQUID 2001 and is folded back in thevicinity of the SQUID 2001. That is, the control line 2004 is wired onthe side of the folded-back part opposite to the side thereof on whichthe SQUID 2001 is located. As described above, the structures of thecontrol line 2004 and the superconducting loop 2009 in this exampleembodiment are similar to those in the third example embodiment (theexample embodiment of a distributed constant-type quantum bit).

This example embodiment also includes the superconducting loop 2009surrounding the SQUID 2001, so that it provides an advantageous effectthat the effect of the crosstalk that is caused as a current flowsthrough the GND plane can be reduced. Further, for a reason similar tothat in the third example embodiment, the occurrence of a shieldingcurrent in the superconducting loop 2009, which would otherwise becaused by the input of the control current to the control line 2004, issuppressed, and the resonance frequency is prevented from being set(i.e., changed) to an unintended frequency.

Seventh Example Embodiment

Next, another example embodiment for reducing the effect of crosstalk ina lumped constant-type quantum bit will be described. FIG. 33 shows alayout of a lumped constant-type quantum bit according to a seventhexample embodiment. Differences from the fifth example embodiment willbe described hereinafter in detail. As shown in FIG. 33 , unlike thefifth example embodiment, the control line 2004 does not separate intobranches in this example embodiment. Further, in this exampleembodiment, a superconducting loop 2009 is formed by air bridges 2007 a,2007 b and 2007 c so as to surround the outside of the SQUID 2001. Thatis, in this example embodiment, the superconducting loop 2009 is acircuit made of a superconductor using the GND plane 2006 and the airbridges 2007 a, 2007 b and 2007 c. Further, a control line 2004 has sucha shape that it enters the superconductor loop 2009 from the outsidethereof, and then goes out from the superconductor loop 2009 again. Thatis, the control line 2004 is wired in a straight line and intersectswith the electrode 2008 connected to the SQUID 2001 in athree-dimensional manner (i.e., like an overpass). Note that the controlline 2004 may be wired in a straight line and intersect with the SQUID2001 in a three-dimensional manner. More specifically, as shown in FIG.33 , an air bridge 2007 d is provided in the middle of the control line2004 to cross over (i.e., cross above) the electrode 2008 or the SQUID2001. That is, the control line 2004 and the electrode 2008, or thecontrol line 2004 and the SQUID 2001 intersect with each other in athree-dimensional manner by the air bridge 2007 d. In this exampleembodiment, the air bridge 2007 a is provided in the vicinity of theterminal of the SQUID 2001 on the side thereof on which the electrode2005 is located as in the case of the fifth example embodiment. The airbridges 2007 b and 2007 c connect parts of the GND plane 106 located onboth sides of the control line 2004 to each other. The air bridges 2007b and 2007 c are provided on both sides of the place where the controlline 2004 and the electrode 2008, or the control line 2004 and the SQUID2001 intersect with each other in a three-dimensional manner.

Note that the positional relationship among the SQUID 2001, theelectrode 2005, and the control line 2004 is, for example, as shown inFIG. 33 and will be described hereinafter. The electrode 2005, the SQUID2001, and the electrode 2008 are arranged in a first direction (theup/down direction in the drawing) in the vicinity of the SQUID 2001.Further, the control line 2004 extends in a second direction (theleft/right direction in the drawing) in the vicinity of the SQUID 2001while intersecting the electrode 2008 or the SQUID 2001 in athree-dimensional manner. In other words, the control line 2004 is wiredso as to cross over the electrode 2008 or the SQUID 2001 in a directionintersecting the direction in which the electrode 2005 and the SQUID2001 are arranged. As described above, the structures of the controlline 2004 and the superconducting loop 2009 in this example embodimentare similar to those in the fourth example embodiment (the exampleembodiment of a distributed constant-type quantum bit).

This example embodiment also includes the superconducting loop 2009surrounding the SQUID 2001, so that it provides an advantageous effectthat the effect of the crosstalk that is caused as a current flowsthrough the GND plane can be reduced. Further, for a reason similar tothat in the fourth example embodiment, the occurrence of a shieldingcurrent in the superconducting loop 2009, which would otherwise becaused by the input of the control current to the control line 2004, issuppressed, and the resonance frequency is prevented from being set(i.e., changed) to an unintended frequency.

The fifth to seventh example embodiments have been described above. Thelumped constant-type circuit shown in these example embodiments, i.e.,an oscillator including a quantum bit having the above-describedconfiguration, can also be expressed as follows. The oscillator includesa GND plane (a GND plane 2006), a conductive member (an electrode 2005),a SQUID (a SQUID 2001), a first connection circuit (air bridge 2007 a),and a superconducting loop circuit (a superconducting loop 2009). Notethat the GND plane is formed of a superconductor. Further, theconductive member is spaced apart from and surrounded by the GND plane.Note that, in this oscillator, a capacitor (a capacitor 2003) is formedby the gap between the GND plane and the conductive member. Further, oneend of the SQUID is connected to the conductive member and the other endthereof is connected to the GND plane. The first connection circuit is asuperconductor circuit that connects parts of the GND plane located onboth sides of the vicinity of the connection part between the conductivemember and the SQUID to each other. Further, the superconducting loopcircuit is a circuit using the GND plane and the first connectioncircuit, and surrounds the SQUID. According to the above-describedoscillator, it is possible to reduce the effect of the crosstalk that iscaused as a current flows through the GND plane by the superconductingloop surrounding the SQUID. Further, in this oscillator, a control line(a control line 2004) may be disposed so that, by a control signalflowing through the control line, two types of magnetic fluxes havingmagnitudes equal to each other and directions opposite to each otherpass through the superconducting loop circuit. This control line ismagnetically coupled with the SQUID, and a control signal is input tothe control line. Note that the magnitudes of the above-described twotypes of magnetic fluxes do not have to be exactly equal to each other,and may include some errors. That is, these two types of magnetic fluxesmay be those having magnitudes roughly equal to each other. For example,the difference between them may be equal to or smaller than 10% of themagnitude of either one of them. In this way, the occurrence of ashielding current in the superconducting loop circuit, which wouldotherwise be caused by the input of the control signal to the controlline, is suppressed, and the resonance frequency is prevented from beingset (i.e., changed) to an unintended frequency.

Further, in particular, the oscillator shown in the fifth exampleembodiment can also be described as an oscillator having the followingfeatures. That is, in the oscillator shown in the fifth exampleembodiment, the control line is divided into a first branch line and asecond branch line at a branch point on the control line. Note that thefirst branch line is wired along the SQUID, and the second branch lineis wired in the direction opposite to the direction of the first branchline. Further, the superconducting loop circuit is a circuit using theGND plane, the first connection circuit, and the first and second branchlines. Further, the length of the first branch line used for thesuperconducting loop circuit is equal to that of the second branch lineused for the superconducting loop circuit. Note that the lengths of thefirst and second branch lines do not have to be exactly equal to eachother, and may include some errors. That is, the lengths of these twolines may be roughly equal to each other. For example, the differencebetween them may be equal to or smaller than 10% of the length of eitherone of them. According to this configuration, it is possible to providean example of a layout of a control line in which, by a control signalflowing through the control line, two types of magnetic fluxes havingmagnitudes roughly equal to each other and directions opposite to eachother pass through the superconducting loop circuit. Note that thisoscillator may include a connection circuit that connects parts of theGND plane located on both sides of the control line to each other (suchas the air bridge 2007 b that connects parts of the GND plane across thecontrol line).

Further, in particular, the oscillator shown in the sixth exampleembodiment can also be described as an oscillator having the followingfeatures. That is, in the oscillator shown in the sixth exampleembodiment, the control line is wired in a U-shape so as to is foldedback in the vicinity of the SQUID. Further, this oscillator alsoincludes a second connection circuit made of a superconductor thatconnects parts of the GND plane located on both sides of the twostraight sections, i.e., the outward and returning sections, of theU-shaped control line to each other (i.e., the air bridge 2007 b thatconnects parts of the GND plane across the control line). Further, thesuperconducting loop circuit is a circuit using the GND plane and thefirst and second connection circuits. According to this configuration,it is possible to provide an example of a layout of a control line inwhich, by a control signal flowing through the control line, two typesof magnetic fluxes having magnitudes equal to each other and directionsopposite to each other pass through the superconducting loop circuit.

Further, in particular, the oscillator shown in the seventh exampleembodiment can also be described as an oscillator having the followingfeatures. That is, in the oscillator shown in the seventh exampleembodiment, the control line is wired in a straight line and intersectswith a connection conductive member (the electrode 2008) for connectingthe other end of the SQUID to the GND plane, or with the SQUID in athree-dimensional manner. Further, this oscillator also includes asecond connection circuit made of a superconductor that connects partsof the GND plane located on both sides of the control line to each other(i.e., the air bridges 2007 b and 2007 c that connect parts of the GNDplane across the control line). The second connection circuit isprovided on each of both sides of the place where the control line andthe connection conductive member, or the control line and the SQUIDintersect with each other in a three-dimensional manner. Further, thesuperconducting loop circuit is a circuit using the GND plane and thefirst and second connection circuits. According to the above-describedconfiguration, it is possible to provide an example of a layout of acontrol line in which, by a control signal flowing through the controlline, two types of magnetic fluxes having magnitudes equal to each otherand directions opposite to each other pass through the superconductingloop circuit.

First Modified Example of Fifth to Seventh Example Embodiments

The below-described modified example can be provided for theabove-described fifth to seventh example embodiments. Note that althougha modified example of the fifth example embodiment will be describedhereinafter, similar modified examples can be implemented for the sixthand seventh example embodiments.

FIG. 34 shows an equivalent circuit of a lumped constant-type quantumbit 2000 according to a first modified example of the fifth exampleembodiment. This quantum bit 2000 differs from the lumped constant-typequantum bit 2000 shown in FIG. 27 because a linear inductor 2010 isinserted in the loop formed by the SQUID 2001 and the capacitor 2003.The lumped constant-type quantum bit 2000 shown in FIG. 27 has a problemthat its nonlinearity is too high to be applied to a quantum computer.Note that the nonlinearity of a circuit that constitutes a quantum bitis quantified by a coefficient (a nonlinear coefficient) defined by acoefficient of a nonlinear term of a Hamiltonian of the circuitconstituting the quantum bit. In the quantum bit 2000 shown in FIG. 34 ,the nonlinear coefficient can be adjusted by the inductance of thelinear inductor 2010. Further, therefore, it is possible to reduce thenonlinearity without increasing the capacitance of the capacitor 2003,and thereby to prevent the loss in the circuit constituting the quantumbit from increasing. FIG. 35 shows a layout of the quantum bit 2000shown in FIG. 34 . The layout shown in FIG. 35 differs from the layoutshown in FIG. 29 because the shape of the electrode 2005 is adjusted sothat the electrode 2005 has a predetermined linear inductance value. Asdescribed above, the electrode 2005 is used as the linear inductorhaving the predetermined inductance in this modified example.Specifically, in the example shown in FIG. 35 , the linear inductance ofthe electrode 2005 is increased compared to that in the layout shown inFIG. 29 by reducing the width of each of the cross-shaped arms of theelectrode 2005 as compared to that in FIG. 29 . The layout shown in FIG.35 is similar to the layout shown in FIG. 29 , except for theabove-described point. Therefore, in this modified example, the effectof the crosstalk that is caused as a current flows through the GND planecan be reduced, and the resonance frequency can be prevented from beingset (i.e., changed) to an unintended frequency due to the shieldingcurrent generated in the superconducting loop caused by the controlcurrent.

Note that, as shown in FIG. 36 , an air bridge 2007 b that connectsparts of the GND plane 2006 located on both sides of the core line ofthe non-branched part of the control line 2004 to each other may befurther added.

Second Modified Example of Fifth to Seventh Example Embodiments

The below-described modified example can be provided for theabove-described fifth to seventh example embodiments. Note that althougha modified example of the fifth example embodiment will be describedhereinafter, similar modified examples can be implemented for the sixthand seventh example embodiments.

FIG. 37 shows an equivalent circuit of a lumped constant-type quantumbit 2000 according to a second modified example in accordance with thefifth example embodiment. This quantum bit 2000 differs from the lumpedconstant-type quantum bit 2000 shown in FIG. 27 because a Josephsonjunction 2011 is inserted in the loop formed by the SQUID 2001 and thecapacitor 2003. As described above, the lumped constant-type quantum bit2000 shown in FIG. 27 has the problem that its nonlinearity is too highto be applied to a quantum computer. In the quantum bit 2000 shown inFIG. 37 , the nonlinear coefficient can be adjusted by adding theJosephson junction 2011 in the loop formed by the SQUID 2001 and thecapacitor 2003. Further, since there is no need to increase thecapacitance of the capacitor 2003 in order to reduce the nonlinearity,it is also possible to prevent the loss in the circuit constituting thequantum bit from increasing. FIG. 38 shows a layout of the quantum bit2000 shown in FIG. 37 . The layout shown in FIG. 38 differs from thelayout shown in FIG. 29 because the Josephson junction 2011 is added inthe middle of the narrow electrode 2008. That is, the SQUID 2001 isconnected to the GND plane 2006 through the Josephson junction 2011 inthis modified example. The layout shown in FIG. 37 is similar to thelayout shown in FIG. 29 , except for the above-described point.Therefore, in this modified example, the effect of the crosstalk that iscaused as a current flows through the GND plane can be reduced, and theresonance frequency can be prevented from being set (i.e., changed) toan unintended frequency due to the shielding current generated in thesuperconducting loop caused by the control current.

Note that, as shown in FIG. 39 , an air bridge 2007 b that connectsparts of the GND plane 2006 located on both sides of the core line ofthe control line 2004 to each other may be further added.

Third Modified Example of Fifth to Seventh Example Embodiments

The below-described modified example can be provided for theabove-described fifth to seventh example embodiments. This modifiedexample differs from the above-described fifth to seventh exampleembodiments because the critical current values of two Josephsonjunctions 2002 a and 2002 b constituting the SQUID 2001 are set tovalues different from each other. By using the above-describedconfiguration, it is possible to provide an inflection point in afunction that represents a relationship between the resonance frequencyof the loop circuit formed by the SQUID 2001 and the capacitor 2003 andthe magnetic field applied to the SQUID 2001 (i.e., a function thatrepresents the dependence of the resonance frequency on the magneticfield). Therefore, by operating the quantum bit 2000 while setting thisinflection point as the operating point, it is possible to suppress theimbalance of the changes of the resonance frequency caused by theperiodic changes of the magnetic field caused by the AC (AlternatingCurrent) control signal. Therefore, it is possible to reduce the adverseeffect which is caused when changes in the resonance frequency areunbalanced. Note that, for example, the area (i.e., the size) of theJosephson junction may be changed in order to change the criticalcurrent value of the Josephson junction. That is, by using two Josephsonjunctions having areas (i.e., sizes) different from each other, it ispossible to realize Josephson junctions 2002 a and 2002 b havingcritical current values different from each other.

Therefore, in this modified example, the effect of the crosstalk that iscaused as a current flows through the GND plane can be reduced, and theresonance frequency can be prevented from being set (i.e., changed) toan unintended frequency due to the shielding current generated in thesuperconducting loop caused by the control current.

Note that, in this modified example, an air bridge 2007 b that connectsparts of the GND plane 2006 located on both sides of the core line ofthe control line 2004 to each other may also be further added.

Eighth Example Embodiment

A distributed constant-type or lumped constant-type quantum bit formedon a chip has been described so far. However, a configuration forreducing crosstalk may be realized in a configuration in which a chipincluding a quantum circuit formed therein is flip-chip connected to asubstrate such as an interposer. That is, instead of using the airbridges as described above, bumps for connecting a chip to a substrateand wiring lines provided on the substrate may be used. Such aconfiguration will be described as an eighth example embodiment. Notethat the flip-chip connection may also be referred to as flip-chipmounting.

In this example embodiment, the circuit described in the fifth exampleembodiment is realized in a configuration in which a chip 2018 isflip-chip connected to a substrate 2019. FIG. 40 shows the chip 2018 onwhich a part of a quantum bit 2000 is formed. On this chip 2018, a GNDplane 2006, an electrode 2005, a SQUID 2001, and the like are formed byusing a superconducting material. Since the arrangement of thesecomponents are similar to that in the fifth example embodiment, thedescription thereof is omitted. The equivalent circuit of the circuitaccording to this example embodiment is similar to that shown in FIG. 27, and a part of this equivalent circuit is formed on the chip 2018.Specifically, the GND plane 2006, the electrode 2005, the SQUID 2001,and the electrode 2008 are formed on the chip 2018. Further, on the chip2018, a capacitor 2003 is formed by the gap between the GND plane 2006and the electrode 2005. The chip 2018 is flip-chip connected to asubstrate such as an interposer by using bumps, and symbols 2012 a and2012 b in FIG. 40 indicate places at which these bumps are connected. Asshown in FIG. 40 , these bumps (bumps 2022 a and 2022 b described later)are provided on both sides of the vicinity of the connection partbetween the electrode 2005 and the SQUID 2001. That is, the positions ofthese bumps correspond to the places at which the air bridge 2007 aconnects parts of the GND plane 2006 to each other in the fifth exampleembodiment.

FIG. 41 shows the substrate 2019 such as an interposer to which the chip2018 is flip-chip connected. In the flip-chip connection, the chip 2018shown in FIG. 40 and the substrate 2019 shown in FIG. 41 are connectedto each other through the bumps (the bumps 2022 a and 2022 b describedlater) so that the surface of the chip 2018 and the surface of thesubstrate 2019 are opposed to each other. On the substrate 2019, a GNDplane 2015 of the substrate and a control line 2016 are formed by usinga superconducting material. The tip of the control line 2016 separatesinto a first branch line 2017 a and a second branch line 2017 b at abranch point 20170. Further, the first branch line 2017 a is disposednear the SQUID 2001 so that the first branch line 2017 a and the SQUID2001 magnetically couple with each other. Meanwhile, the second branchline 2017 b is disposed far from the SQUID 2001 in order to prevent thesecond branch line 2017 b and the SQUID 2001 magnetically coupling witheach other. Specifically, in order to make the first branch line 2017 aand the SQUID 2001 magnetically couple with each other while preventingthe second branch line 2017 b and the SQUID 2001 from magneticallycouple with each other, these branch lines are wired (i.e., routed) asfollows. That is, the first branch line 2017 a of the substrate 2019 iswired along the SQUID 2001 of the chip 2018, and the second branch line2017 b of the substrate 2019 is wired along the electrode 2008 of thechip 2018 in the direction opposite to the direction of the first branchline 2017 a. The first and second branch lines 2017 a and 2017 b areboth connected to the GND plane 2015. The first and second branch lines2017 a and 2017 b are lines symmetrical to each other in the left/rightdirection, and in the example shown in FIG. 41 , they are shaped so asto curve in directions opposite to each other. Specifically, the firstand second branch lines 2017 a and 2017 b extend a predetermined lengthfrom the branch point 20170 in a first direction (the up/down directionin the drawing), and then their tips extend a predetermined length inthe direction in which the non-branched part of the control line 2016extends from the branch point 20170 (i.e., the left direction in thedrawing). That is, in the example shown in FIG. 41 , the first andsecond branch lines 2017 a and 2017 b are folded back in the directionin which the non-branched part extends. However, the above-describedconfiguration is merely an example, and the first and second branchlines 2017 a and 2017 b may not be folded back. That is, the controlline 2016 may be a T-shaped line that separates into the first andsecond branch lines 2017 a and 2017 b at the branch point 20170. Notethat the non-branched part of the control line 2016 means the part ofthe control line 2016 other than the first and second branch lines 2017a and 2017 b. The non-branched part of the control line 2016 extends ina second direction (the left/right direction in the drawing) in thevicinity of the SQUID 2001. Specifically, in the example shown here, ascan be seen in FIGS. 40 and 41 , the non-branched part of the controlline 2016 extends so as to cross the connection part between the SQUID2001 and the electrode 2008.

In FIG. 41 , symbols 2013 a and 2013 b indicate places at which theabove-described bumps are connected. Note that although the connectionplaces of the bumps indicated by the symbols 2013 a and 2013 b arelocated inside the bridge electrode (the conductive member) 2014 aroundwhich a gap is provided in the example shown in FIG. 41 , the gap doesnot necessarily have to be provided around the bridge electrode 2014.That is, the bumps may be connected to the GND plane 2015. Note that thebridge electrode 2014 is made of a superconductor.

FIG. 42 shows a cross-sectional diagram of a structure in which the chip2018 and the substrate 2019 are flip-chip connected to each other byusing the bumps 2022 a and 2022 b. Specifically, it shows across-sectional diagram taken along a line A-A′ in FIGS. 40 and 41 .Note that, in FIG. 42 , a symbol 2020 indicates a silicon substrate ofthe chip 2018, and a symbol 2021 indicates a silicon substrate of thesubstrate 2019. Further, as shown in FIG. 42 , the distance between thechip 2018 and the substrate 2019 is represented by d. Further, althoughit is not explicitly shown in FIG. 42 , the substrate 2019 may furtherinclude TSVs (Through Silicon Vias; through silicon electrode). The TSVscan, for example, serve to electrically connect a GND plane formed onthe rear surface of the substrate 2019 (the bottom side (i.e., theunderside) of the substrate 2019 in FIG. 42 ) to a GND plane 2015 formedon the front surface of the substrate 2019 (the top side of thesubstrate 2019 in FIG. 42 ). The TSVs can serve to electrically connect,for example, a control line formed on the rear surface of the substrate2019 to a control line 2016 formed on the front surface of the substrate2019. As shown in FIG. 42 , an electrically-connected circuit expressedas “the GND plane 2006 of the chip 2018 - the bump 2022 a - the bridgeelectrode 2014 of the substrate 2019 - the bump 2022 b - the GND plane2006 of the chip 2018″ is formed, and this circuit provides a functionsimilar to that of the air bridge. Therefore, a superconducting loop2009 that surrounds the outside of the SQUID 2001 is formed by using theGND plane 2006 of the chip 2018, the bumps 2022 a and 2022 b, and thebridge electrode 2014 of the substrate 2019. Therefore, in this exampleembodiment, it is also possible to reduce the effect of the crosstalkthat is caused as a current flows through the GND plane.

Note that when a control signal is input from the control line 2016shown in FIG. 41 , the control signal is divided and flows into thefirst and second branch lines 2017 a and 2017 b. Since the first branchline 2017 a is positioned directly below the SQUID 2001 in FIG. 40 , theSQUID 2001 senses (i.e., is affected by) the magnetic flux generated bythe current flowing through the first branch line 2017 a. Meanwhile,since the second branch line 2017 b is not positioned directly below theSQUID 2001, the current flowing through the second branch line 2017 bhardly affects the SQUID 2001. Further, since the first and secondbranch lines 2017 a and 2017 b are shaped so as to curve in directionsopposite to each other, the magnetic fluxes generated by the currentsflowing through the first and second branch line 2017 a and 2017 b have,inside the two branch lines, magnitudes equal to each other anddirections opposite to each other. Therefore, in this exampleembodiment, the resonance frequency can also be prevented from being set(i.e., changed) to an unintended frequency due to the shielding currentgenerated in the superconducting loop caused by the control current.

Note that, in FIGS. 40 to 42 , an example in which a lumpedconstant-type quantum bit having a configuration in which a control lineseparates into branches as in the case of the fifth example embodimentis shown. However, the configuration using flip-chip connection can alsobe applied to the previously-described various quantum bits in a similarmanner. For example, the configuration using flip-chip connection canalso be applied to a lumped constant-type quantum bit using a controlline having other shapes, or to a distributed constant-type quantum bit.Some examples of such other configurations of quantum bits usingflip-chip connection will be described hereinafter.

A configuration of a chip and a substrate in which parts of a GND planelocated on both sides of a control line are connected to each other asshown in FIG. 30 will be described. FIG. 43 shows a layout of a chip ina case where parts of a GND plane located on both sides of a controlline are connected to each other. Further, FIG. 44 shows a layout of asubstrate in a case where parts of a GND plane located on both sides ofa control line are connected to each other. Differences from those shownin above-described FIGS. 40 and 41 will be described hereinafter. Torealize the connection between parts of the GND plane 2015 on both sidesof the control line 2016, bumps for connecting the parts of the GNDplane 2015 on both sides of the control line 2016 on the substrate 2019to the bridge electrodes (the conductive members) 2014 a of the chip2018 are provided between the chip 2018 and the substrate 2019. In FIG.43 , symbols 2012 c and 2012 d indicate the connection places of thesebumps on the chip 2018. Further, in FIG. 44 , symbols 2013 c and 2013 dindicate the connection places of these bumps on the substrate 2019.Note that although the connection places of the bumps are located insidethe bridge electrode 2014 a around which a gap is provided in theexample shown in FIG. 43 , the gap does not necessarily have to beprovided around the bridge electrode 2014 a. That is, the bumps may beconnected to the GND plane 2006. Note that the bridge electrode 2014 ais made of a superconductor. Therefore, the above-described bumps andthe bridge electrode 2014 a of the chip 2018 can serve as the air bridge2007 b in FIG. 30 . As described above, by flip-chip connecting the chipshown in FIG. 43 and the substrate shown in FIG. 44 to each other, aconfiguration similar to that in the example embodiment shown in FIG. 30can be realized by a three-dimensional circuit, and advantageous effectssimilar to those in the example embodiment in FIG. 30 can be obtained.

Next, a configuration of a chip and a substrate in which a U-shapedcontrol line is used as shown in FIG. 32 will be described. FIG. 45shows a layout on a chip in which a U-shaped control line is used.Further, FIG. 46 shows a layout on a substrate in which a U-shapedcontrol line is used. Differences from those shown in above-describedFIGS. 40 and 41 will be described hereinafter.

FIG. 45 shows a chip 2018 on which a part of a quantum bit 2000 isformed. On this chip 2018, a GND plane 2006, an electrode 2005, and aSQUID 2001 are formed by using a superconducting material. Since thearrangement of these components are similar to that in the sixth exampleembodiment, the description thereof is omitted. In FIG. 45 , symbols2012 a and 2012 b indicate places at which bumps are connected, andthese places are similar to those shown in FIG. 40 .

FIG. 46 shows a substrate 2019 such as an interposer to which the chip2018 is flip-chip connected. On the substrate 2019, a GND plane 2015 ofthe substrate and a control line 2016 are formed by using asuperconducting material. When the projection of the later-describedsuperconducting loop 2009 onto the substrate 2019 is considered, thecontrol line 2016 has such a shape that it enters the projectedsuperconductor loop 2009 from the outside thereof, is folded back insidethe superconductor loop 2009, and then goes out from the superconductorloop 2009 again. That is, the control line 2016 is wired in a U-shape sothat it is folded back in the vicinity of the SQUID 2001. The controlline 2016 extends in a second direction (the left/right direction in thedrawing) in the vicinity of the SQUID 2001, and is folded back in thevicinity of the SQUID 2001.

In FIG. 46 , symbols 2013 a and 2013 b indicate places at which theabove-described bumps are connected. Note that although the connectionplaces of the bumps indicated by the symbols 2013 a and 2013 b arelocated inside the bridge electrode (the conductive member) 2014 aroundwhich a gap is provided in the example shown in FIG. 46 , the gap doesnot necessarily have to be provided around the bridge electrode 2014.That is, the bumps may be connected to the GND plane 2015. Note that thebridge electrode 2014 is made of a superconductor.

As can be seen from FIGS. 45 and 46 , an electrically-connected circuitexpressed as “the GND plane 2006 of the chip 2018 - the bump - thebridge electrode 2014 of the substrate 2019 - the bump - the GND plane2006 of the chip 2018” is formed. Therefore, a superconducting loop 2009that surrounds the outside of the SQUID 2001 is formed by using the GNDplane 2006 of the chip 2018, the bumps, and the bridge electrode 2014 ofthe substrate 2019. Note that, as obvious from the above-described fact,in the configuration using flip-chip connection, the structure thatserves as the air bridge 2007 b in FIG. 32 is unnecessary.

As described above, by flip-chip connecting the chip shown in FIG. 45 tothe substrate shown in FIG. 46 to each other, a configuration similar tothat in the sixth example embodiment can be realized by athree-dimensional circuit, and advantageous effects similar to those inthe sixth example embodiment can be obtained.

Next, a configuration of a chip and a substrate in which a straightcontrol line is used as shown in FIG. 33 will be described. FIG. 47shows a layout on a chip in which a straight control line is used.Further, FIG. 48 shows a layout on a substrate in which a straightcontrol line is used. Differences from those shown in above-describedFIGS. 40 and 41 will be described hereinafter.

FIG. 47 shows a chip 2018 on which a part of a quantum bit 2000 isformed. On this chip 2018, a GND plane 2006, an electrode 2005, a SQUID2001, and an electrode 2008 are formed by using a superconductingmaterial. Since the arrangement of these components are similar to thatin the seventh example embodiment, the description thereof is omitted.In FIG. 47 , symbols 2012 a and 2012 b indicate places at which bumpsare connected, and these places are similar to those shown in FIG. 40 .

FIG. 48 shows a substrate 2019 such as an interposer to which the chip2018 is flip-chip connected. On the substrate 2019, a GND plane 2015 ofthe substrate and a control line 2016 are formed by using asuperconducting material. When the projection of the later-describedsuperconducting loop 2009 onto the substrate 2019 is considered, thecontrol line 2016 has such a shape that it enters the projectedsuperconductor loop 2009 from the outside thereof, and then goes outfrom the superconductor loop 2009 again. That is, the control line 2016is wired in a straight line above the electrode 2008 connected to theSQUID 2001, or above the SQUID 2001. The control line 2016 extends in asecond direction (the left/right direction in the drawing) in thevicinity of the SQUID 2001 while intersecting the electrode 2008 or theSQUID 2001 in a three-dimensional manner (i.e., like an overpass). Inother words, the control line 2016 is wired so as to cross over (i.e.,cross above) the electrode 2008 or the SQUID 2001 in a directionintersecting the direction in which the electrode 2005 and the SQUID2001 are arranged.

In FIG. 48 , symbols 2013 a and 2013 b indicate places at which theabove-described bumps are connected. Note that although the connectionplaces of the bumps indicated by the symbols 2013 a and 2013 b arelocated inside the bridge electrode (the conductive member) 2014 aroundwhich a gap is provided in the example shown in FIG. 48 , the gap doesnot necessarily have to be provided around the bridge electrode 2014.That is, the bumps may be connected to the GND plane 2015. Note that thebridge electrode 2014 is made of a superconductor.

As can be seen in FIGS. 47 and 48 , an electrically-connected circuitexpressed as “the GND plane 2006 of the chip 2018 - the bump - thebridge electrode 2014 of the substrate 2019 - the bump - the GND plane2006 of the chip 2018” is formed. Therefore, a superconducting loop 2009that surrounds the outside of the SQUID 2001 is formed by using the GNDplane 2006 of the chip 2018, the bumps, and the bridge electrode 2014 ofthe substrate 2019. Note that, as obvious from the above-described fact,in the configuration using flip-chip connection, the structure thatserves as the air bridges 2007 b and 2007 c in FIG. 33 is unnecessary.

As described above, by flip-chip connecting the chip shown in FIG. 47 tothe substrate shown in FIG. 48 to each other, a configuration similar tothat in the seventh example embodiment can be realized by athree-dimensional circuit, and advantageous effects similar to those inthe seventh example embodiment can be obtained.

Ninth Example Embodiment

Another example embodiment of a configuration in which a chip 2018 isflip-chip connected to a substrate 2019 will be described as a ninthexample embodiment. Before describing details of the ninth exampleembodiment, firstly, the eighth example embodiment will be examined.

FIG. 49 is a diagram that is obtained by adding a drawing forexplanation in the layout shown in FIG. 41 . Specifically, it is adiagram in which a drawing in which the SQUID 2001 of the chip 2018 isprojected onto the substrate 2019 is added. Note that a drawing in whichthe SQUID 2001 of the chip 2018 is projected onto the substrate 2019 isadded is also added in some of the later-described drawings.

As shown in FIG. 49 , on a substrate 2019 according to the eighthexample embodiment, a superconducting loop 2500, which is closed on thesubstrate 2019, is formed. This superconducting loop 2500 is asuperconducting loop different from any of the superconducting loops2009 described above. In the configuration where the chip 2018 isflip-chip connected to the substrate 2019, when the quantum circuit isoperated, a current could flow to the GND plane 2015 of the substrate2019. This phenomenon occurs because, for example, when a controlcurrent is input to the control line 2016 on the substrate 2019, thecontrol current flows to the GND plane 2015 of the substrate 2019 afterflowing through the control line 2016. A configuration for reducingcrosstalk that is caused as a current flows through the GND plane 2006of the chip 2018 has been described so far. In contrast, a configurationfor reducing crosstalk that is caused as a current flows through the GNDplane 2015 of the substrate 2019 will be described in the ninth exampleembodiment.

FIG. 50 is a diagram for explaining a problem that occurs when a currentIR1, which causes crosstalk, has flowed to the GND plane 2015 of thesubstrate 2019 shown in FIG. 49 . In this case, a part of the magneticflux G10 generated by the current IR1 passes through the superconductingloop 2500 of the substrate 2019. Since the magnetic flux that passesthrough inside the superconducting loop 2500 of the substrate 2019 mustbe conserved, a shielding current IS1 flows as shown in FIG. 50 . As aresult, the current IS1 generates a magnetic flux G11, and a part of themagnetic flux G11 that is generated inside the superconducting loop 2500of the substrate 2019 cancels the part of the magnetic flux G10 that isgenerated inside the superconducting loop 2500 of the substrate 2019 bythe current IR1. However, since the shielding current IS1 passes throughan area very close to the SQUID 2001 as shown in FIG. 50 , there is apossibility that the SQUID 2001 on the chip 2018 could sense (i.e., beaffected by) a part of the magnetic flux G11 generated by the shieldingcurrent IS1. As a result, the SQUID 2001 is unintentionally controlled(e.g., the resonance frequency of the quantum bit is unintentionallychanged). The layout on the substrate is preferably designed so thatsuch a possibility is eliminated as much as possible.

FIG. 51 shows an example of such a layout of a substate, and shows alayout of the substrate 2019 according to the ninth example embodiment.In the configuration shown in FIG. 51 , a superconducting loop 2600 isformed by using bumps for connecting the GND plane 2015 of the substrate2019 to the GND plane 2006 of the chip 2018. In FIG. 51 , symbols 2012 eand 2012 f indicate places at which these bumps are connected. As shownin FIG. 51 , in this example embodiment, a part of the GND plane 2015corresponding to the area of the SQUID 2001 projected onto the substrate2019 and its surrounding area is cut out. That is, the GND plane 2015 isshaped as if a part having a predetermined shape (i.e., a rectangle inthe example shown in FIG. 51 ) is cut out from the GND plane 2015 sothat the GND plane 2015 is spaced apart from the SQUID 2001 projectedonto the substrate 2019 by a predetermined interval. Note that, in thisexample embodiment, in order to secure the path of the control line2016, the GND plane 2015 is shaped as if the outside of theaforementioned rectangle is cut out along the control line 2016.

The superconducting loop 2600 is a loop circuit having a shapecorresponding to the periphery of the above-described rectangle, and isa three-dimensional superconducting loop using the substrate 2019, theabove-described bumps, and the chip 2018. In FIG. 51 , as indicated bysymbols 2012 e and 2012 f, the bumps are provided on both sides of thecontrol line 2016 so as to form a superconducting loop 2600 across thecontrol line 2016. Specifically, in the example shown in FIG. 51 , theyare provided in the vicinity of the aforementioned rectangle. By theabove-described configuration, a three-dimensional superconducting loop2600 using the GND plane 2015 of the substrate 2019, the bumps, and theGND plane 2006 of the chip 2018 is formed. Note that the line crossingover the control line 2016 in the superconducting loop 2600 is realized(i.e., formed) by using the bumps and the GND plane 2006 of the chip2018, and the other lines in the superconducting loop 2600 are realized(i.e., formed) by the GND plane 2015 of the substrate 2019. That is, thesuperconducting loop 2600 is a circuit that uses the GND plane 2015 ofthe substrate 2019 and the connection circuit (the bumps and the GNDplane 2006 of the chip 2018) that connects parts of the GND plane 2015of the substrate 2019 located on both sides of the control line 2016 toeach other. Note that, as shown in FIG. 51 , the superconducting loop2600 is a circuit that surrounds the area in the substrate 2019corresponding to the area where the SQUID 2001 is located (the areawhere the projected SQUID 2001 is located) with a predetermined interval(see g1, g2, g3 and g4 in FIG. 51 ) therebetween. The control line 2016does not separate into branches, and is a straight line. The controlline 2016 enters the superconducting loop 2600 of the substrate 2019from the outside thereof, and connects to the superconducting loop 2600(the GND plane 2015 of the substrate 2019). That is, the straightcontrol line 2016 is provided so as to cross the superconducting loop2600 (the aforementioned rectangle). More specifically, the control line2016 is wired in a straight line above the electrode 2008 connected tothe SQUID 2001, or above the SQUID 2001. The control line 2016 extendsin a second direction (the left/right direction in the drawing) in thevicinity of the SQUID 2001 while intersecting the electrode 2008 or theSQUID 2001 in a three-dimensional manner (i.e., like an overpass). Inother words, the control line 2016 is wired so as to cross over (i.e.,cross above) the electrode 2008 or the SQUID 2001 in a directionintersecting the direction in which the electrode 2005 and the SQUID2001 are arranged.

According to the configuration in accordance with the ninth exampleembodiment, the superconducting loop 2600 of the substrate 2019 can bedisposed far from the position of the projected SQUID 2001. Therefore,as shown in FIG. 52 , even when the current IR1, which causes crosstalk,flows through the GND plane 2015 of the substrate 2019, the magneticflux G11 generated by the shielding current IS1, which flows through thesuperconducting loop 2600 of the substrate 2019 because of the flow ofthe current IR1, does not affect the SQUID 2001. Alternatively, even ifit affects the SQUID 2001, its effect can be reduced as compared to thatin the configuration of the layout shown in FIG. 50 .

Here, when the distance between the chip and the substrate isrepresented by d (see FIG. 42 ), the distances between the sides of thesuperconducting loop 2600 (the aforementioned rectangle) and therespective sides of the projected SQUID 2001, i.e., the gaps g1, g2, g3and g4 in FIG. 51 , are preferably as long as possible. That is, theseparation distance between the SQUID 2001 and the superconducting loop2600 is preferably as long as possible. For example, the gaps g1, g2, g3and g4 are preferably equal to or longer than d, more preferably equalto or longer than 2d, and even more preferably equal to or longer than3d.

First Modified Example of Ninth Example Embodiment

A first modified example of the ninth example embodiment will bedescribed. Note that descriptions of components/structures similar tothose in the ninth example embodiment are omitted as appropriate. FIG.53 shows a layout of a substrate 2019 according to the first modifiedexample of the ninth example embodiment. Further, FIG. 54 shows across-sectional diagram of a structure in which the chip 2018 and thesubstrate 2019 are flip-chip connected to each other by using bumps 2022a and 2022 b. Specifically, it shows a cross-sectional diagram takenalong a line B-B′ in FIG. 53 . As shown in FIG. 53 , the control line2016 may be disposed only inside the superconducting loop 2600 of thesubstrate 2019. In this case, as shown in FIG. 54 , the control line2016 is configured so as to reach the front surface of the substrate2019 from the rear surface of the substrate 2019 through a TSV 2016 a,which passes (i.e., extends) through the substrate 2019, pass through awiring line for the control line provided on the front surface of thesubstrate 2019, and return to the rear surface of the substrate 2019through a TSV 2016 b. Note that the rear surface of the substrate 2019means the bottom side (i.e., the underside) of the substrate 2019 inFIG. 54 , and the front surface of the substrate 2019 means the top sideof the substrate 2019 in FIG. 54 . Further, in FIG. 54 , a symbol 2016 cindicates a wiring line for the control line provided on the rearsurface of the substrate 2019. Further, in the configuration shown inFIG. 54 , the GND plane 2015 on the front surface of the substrate 2019is connected to the GND plane 2015 b on the rear surface of thesubstrate 2019 through the TSV 2015 a.

In the ninth example embodiment, the superconducting loop 2600 uses, asa part thereof, the GND plane 2006 of the chip 2018. In contrast, inthis modified example, the superconducting loop 2600 is closed on thesubstrate 2019 as shown in FIG. 53 . That is, in this modified example,as shown in FIG. 53 , the superconducting loop 2600 is the GND plane2015 of the substrate 2019, which completely surrounds the area in thesubstrate 2019 corresponding to the area where the SQUID 2001 is locatedwith a predetermined interval therebetween. Even in the above-describedconfiguration, advantageous effects similar to those in the ninthexample embodiment can be obtained.

Second Modified Example of Ninth Example Embodiment

A second modified example of the ninth example embodiment will bedescribed. Note that descriptions of components/structures similar tothose in the first modified example of the ninth example embodiment areomitted as appropriate. FIG. 55 shows a layout of a substrate 2019according to the second modified example of the ninth exampleembodiment.

Since the current flowing through the control line 2016 is a current inwhich a DC current and a high-frequency current such a current having afrequency of 20 GHz are superimposed, a high-frequency signal flowsthrough the control line 2016. Therefore, the transmissioncharacteristics of the control line 2016 at high frequencies preferablyshould be improved. In general, the impedance of a signal sourceapparatus that supplies a signal to the control line 2016 is 50 Ω.Therefore, it is necessary to make the characteristic impedance of thecontrol line 2016 as close as 50 Ω in order to improve the transmissioncharacteristics of the control line 2016 at high frequencies. In thefirst modified example of the ninth example embodiment, since thecontrol line 2016 is somewhat far from the GND plane 2015, thecharacteristic impedance of the control line 2016 could be higher than50 Ω. In particular, as shown in FIG. 53 , the control line 2016 is farfrom the GND plane 2015 on both sides of the control line 2016 (theupper and lower sides of the control line 2016 in FIG. 53 ). In theconfiguration shown in FIG. 53 , if the characteristic impedance of thecontrol line 2016 becomes higher than 50 Ω, it is preferred to lower thecharacteristic impedance of the control line 2016 and thereby to bringit closer to 50 Ω. To that end, it is necessary to dispose the GNDs onboth sides of the control line 2016 closer to the control line 2016 thanin the configuration shown in FIG. 53 . In the second modified exampleof the ninth example embodiment, as shown in FIG. 55 , GNDs (GND lines2015 c) are disposed in places on both sides of the control line 2016that are closer to the control line 2016 than the GND plane 2015 is.That is, GND lines 2015 c are provided on both sides of the control line2016 along the control line 2016. In this way, the characteristicimpedance of the control line 2016 is brought closer to a predeterminedvalue (e.g., 50 Ω). Therefore, it is expected that the transmissioncharacteristics of the control line 2016 at high frequencies willimprove as compared to those in the configuration of the first modifiedexample. Note that the above-described GND lines 2015 c are connected tothe GND plane on the rear surface of the substrate 2019 through TSVs2015 d. Further, the control line 2016 is connected to a wiring line forthe control line on the rear surface of the substrate 2019 through theTSV 2016 a (the TSV 2016 b). Further, the control line 2016 and the GNDlines 2015 c are wired inside the superconducting loop 2600 on thesurface of the substrate 2019 that is opposed to the chip 2018. Further,the control line 2016 is connected to the TSV 2016 a (the TSV 2016 b),which passes (i.e., extends) through the substrate 2019, and the GNDlines 2015 c are connected to the TSVs 2015 d, which passes through thesubstrate 2019. Further, the TSVs 2015 d are disposed (i.e., formed)along the TSV 2016 a (the TSV 2016 b).

Third Modified Example of Ninth Example Embodiment

A third modified example of the ninth example embodiment will bedescribed. Note that descriptions of components/structures similar tothose in the second modified example of the ninth example embodiment areomitted as appropriate. FIG. 56 shows a layout of a substrate 2019according to the third modified example of the ninth example embodiment.Similarly to the above-described second modified example, theconfiguration shown in FIG. 56 is also used to make the characteristicimpedance of the control line 2016 close to a predetermined value (e.g.,50 Ω). In the configuration shown in FIG. 55 , two TSVs 2015 d for theGNDs are disposed on the respective sides (i.e., both sides) of each ofthe TSVs 2016 a and 2016 b for the control line 2016. In contrast, inthe configuration shown in FIG. 56 , four TSVs 2015 d for the GNDs aredisposed around each of the TSVs 2016 a and 2016 b for the control line2016. Note that the GND lines 2015 c are wired so as to surround thecontrol line 2016 on the front surface of the substrate 2019.

It should be noted that, in order to improve the high-frequencycharacteristics of the control line 2016, most preferably, TSVs for theGNDs are arranged so as to completely surround the TSVs for the controlline, and thereby forming a structure of the TSVs similar to that of thecoaxial cable. That is, in order to improve the high-frequencycharacteristics of the control line, it is most preferred to use adual-structure TSV including a hollow cylindrical TSV for the GND and aTSV for the control line that passes through the hollow part of the TSVfor the GND and is electrically insulated from the TSV for GND throughsilicon. However, if it is difficult to form such a coaxial TSV, forexample, as shown in FIG. 56 , the high-frequency characteristics of thecontrol line is improved by arranging four TSVs 2015 d for the GNDsaround the TSV 2016 a (the TSV 2016 b) for the control line 2016 andthereby forming a structure resembling the coaxial structure. Theconfiguration in which four TSVs 2015 d for the GNDs are arranged asshown in FIG. 56 is closer to the coaxial structure than theconfiguration in which two TSVs 2015 d for the GNDs are arranged asshown in FIG. 55 is. Therefore, it is expected that the high-frequencycharacteristics of the control line 2016 will be improved by adoptingthe configuration shown in FIG. 56 rather than adopting theconfiguration shown in FIG. 55 . As described above, a plurality of TSVs2015 d may be provided for one TSV 2016 a (one TSV 2016 b) so as tosurround the TSV 2016 a (the TSV 2016 b). Note that the number of TSVs2015 d surrounding the TSV 2016 a (the TSV 2016 b) is not limited to twoor four, but may be three, or five or more.

Other Modified Example of Ninth Example Embodiment

Other conceivable modified examples of the ninth example embodimentinclude configurations shown in FIGS. 57 and 58 . These examples aresimilar to the ninth example embodiment, except that the control line2016 has a U-shape. That is, as shown in FIG. 57 or FIG. 58 , thecontrol line 2016 may have such a shape that it enters thesuperconductor loop 2600 of the substrate 2019 from the outside thereof,is folded back inside the superconductor loop 2600 of the substrate2019, and then goes out from the superconductor loop 2600 again.Further, in the configurations shown in FIGS. 57 and 58 , the controlline 2016 may be disposed only inside the superconducting loop 2600 ofthe substrate 2019 by using TSVs as in the case of the configurationsshown in FIGS. 53, 55 and 56 .

Note that the present disclosure is not limited to the above-describedexample embodiments, and various modifications can be made to themwithin the scope and spirit of the disclosure. For example, theabove-described oscillator can be used for an arbitrary purpose. Forexample, the above-described oscillator may be used as a phase detector,or as a quantum computer.

According to the present disclosure, an oscillator in which crosstalkcan be reduced can be provided.

The first to ninth embodiments can be combined as desirable by one ofordinary skill in the art.

While the disclosure includes been particularly shown and described withreference to embodiments thereof, the disclosure is not limited to theseembodiments. It will be understood by those of ordinary skill in the artthat various changes in form and details may be made therein withoutdeparting from the spirit and scope of the present disclosure as definedby the claims.

What is claimed is:
 1. An oscillator comprising: a SuperconductingQuantum Interference Device (SQUID); a transmission line connected tothe SQUID; a ground plane; and a first connection circuit connectingparts of the ground plane located on both sides of the transmission lineto each other, wherein the first connection circuit is disposed at aplace a distance of which from a part at which the transmission line andthe SQUID are connected to each other is 1/20 or less of a length of ¼of a wavelength of a standing wave generated on the transmission line.2. The oscillator according to claim 1, further comprising: a controlline configured to magnetically couple with the SQUID, and to which acontrol signal is input; and a second connection circuit connectingparts of the ground plane located on both sides of the control line toeach other.
 3. An oscillator comprising: a component in which twoJosephson junctions are connected in a loop by superconducting lines atransmission line connected to the component; a ground plane; and afirst connection circuit connecting parts of the ground plane located onboth sides of the transmission line to each other, wherein the firstconnection circuit is disposed at a place a distance of which from apart at which the transmission line and the component are connected toeach other is 1/20 or less of a length of ¼ of a wavelength of astanding wave generated on the transmission line.
 4. The oscillatoraccording to claim 3, further comprising: a control line configured tomagnetically couple with the component, and to which a control signal isinput; and a second connection circuit connecting parts of the groundplane located on both sides of the control line to each other.